Topics in graph automorphisms and reconstruction

Topics in Graph Automorphisms and Reconstruction

Volumn , Issue , 2016, Pages 1-192

  Lauri, Josef ^a   Scapellato, Raffaele ^b  

^a UNIVERSITY OF MALTA   (Malta)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85048166722     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9781316669846     Document Type: Book

References (267)

1. U. P. Acharya and H. S. Mehta. “2-Cartesian product of special graphs”. In: Int. J. Math. and Soft Comput. 4.1 (2014), pp. 139-144(cit. on p. 108).
2. Á. Ádám. “Research problem 2-10”. In: J. Combin. Theory 2 (1967), p. 393 (cit. on p. 122).
3. N. Alon, Y. Caro, I. Krasikov, and Y. Roditty. “Combinatorial reconstruction problems”. In: J. Combin. Theory (Ser. B) 47 (1989), pp. 153-161(cit. on p. 169).
4. N. Alon and J. H. Spencer. The Probabilistic Method. Wiley, 1992(cit. on p. 38).
5. B. Alspach. “Point-symmetric graphs and digraphs of prime order and transitive groups of prime degree”. In: J. Combin. Theory (Ser. B) 15 (1973), pp. 12-17 (cit. on p. 122).
6. B. Alspach. “Isomorphism and Cayley graphs on abelian groups”. In: Graph Symmetry: Algebraic Methods and Applications. Ed. by G. Hahn and G. Sabidussi. Kluwer Acad. Publ., 1997, pp. 1-22 (cit. on p. 122).
7. B. Alspach, D. Marusic, and L. A. Nowitz. “Constructing graphs which are 1/2-transitive”. In: J. Austral. Math. Soc. (Ser. A) 56 (1994), pp. 391-402 (cit. on p. 48).
8. B. Alspach and T. D. Parsons. “A construction for vertex-transitive graphs”. In: Canad. J. Math. 34 (1982), pp. 307-318 (cit. on pp. 115, 122).
9. B. Alspach and M.-Y. Xu. “2-arc-transitive graphs of order 3p”. In: J. Algebraic Combin. 3 (1994), pp. 3247-355 (cit. on p. 91).
10. W. C. Arlinghaus and F. Harary. “The digraph number of a finite abelian group”. In: Wiss. Z. Tech. Hochsch. Ilmenau 33.1 (1987), pp. 25-31 (cit. on p. 62).
11. M. Aschbacher. “The nonexistence of rank three permutation groups of degree 3250 and subdegree 57”. In: J. Algebra 19 (1971), pp. 538-540 (cit. on p. 77).
12. K. Asciak. “The degree-associated edge-reconstruction number of disconnected graphs and trees”. Preprint. 2015 (cit. on p. 144).
13. K. Asciak and J. Lauri. “On disconnected graphs with large reconstruction numbers”. In: Ars Combin. 62 (2002), pp. 173-181 (cit. on p. 143).
14. K. Asciak and J. Lauri. “On the edge-reconstruction number of disconnected graphs”. In: Bull. Inst. Combin. and Its Applics. 63 (2011), pp. 87-100 (cit. on p. 143).
15. K. Asciak, J. Lauri, W. Myrvold, and V. Pannone. “On the edge-reconstruction number of a tree”. In: Australas. J. Combin. 60 (2014), pp. 169-190 (cit. on p. 144).
16. L. Babai. “Long cycles in vertex-transitive graphs”. In: J. Graph Theory 3 (1979), pp. 23-29 (cit. on p. 60).
17. L. Babai. “On the abstract group of automorphisms”. In: Combinatorics. Ed. by H. N. V. Temperley. Vol. 52. London Math. Soc. Lecture Note Series. Proceedings of the Eighth British Combinatorial Conference University College Swansea, 1981. Cambridge University Press, 1981, pp. 1-40 (cit. on p. 62).
18. L. Babai. “Automrphism groups, isomorphism, reconstruction”. In: Handbook of Combinatorics. Ed. by R. Graham, M. Grotschel, and L. Lovasz. Vol. 2. Elsevier Science B.V., 1995. Chap. 27, pp. 1447-1540 (cit. on p. 63).
19. D. W. Bange, A. E. Barkauskas, and L. H. Host. “Class-reconstruction of total graphs”. In: J. Graph Theory 11 (1987), pp. 221-230 (cit. on p. 147).
20. M. D. Barrus and D. B. West. “Degree associated reconstruction number of graphs”. In: Discrete Math. 310 (2010), pp. 2600-2612 (cit. on p. 144).
21. R. A. Beaumont and R. P. Peterson. “Set-transitive permutation groups”. In: Canadian J. Math. 7 (1955), pp. 35-42 (cit. on p. 115).
22. M. Behzad, G. Chartrand, and L. Lesniak-Foster. Graphs and Digraphs. Prindle, Weber & Schmidt, 1979 (cit. on pp. 17, 60, 62).
23. L. W. Beineke and E. T. Parker. “On nonreconstructable tournaments”. In: J. Combinatorial Theory 9 (1970), pp. 324-326 (cit. on p. 137).
24. N. L. Biggs. Algebraic Graph Theory. Cambridge University Press, 1993 (cit. on pp. 17, 32, 34, 38, 77, 108, 154).
25. N. L. Biggs and D. H. Smith. “On trivalent graphs”. In: Bull. London Math. Soc. 3 (1971), pp. 155-158 (cit. on p. 38).
26. N. L. Biggs and A. T. White. Permutation Groups and Combinatorial Structures. Cambridge University Press, 1979 (cit. on p. 77).
27. B. Bollobas. “Almost every graph has reconstruction number 3”. In: J. Graph Theory 14 (1990), pp. 1-4 (cit. on p. 38).
28. B. Bollobas. Modern Graph Theory. Springer-Verlag, 1998 (cit. on p. 17).
29. B. Bollobas. Random Graphs. Cambridge University Press, 2001 (cit. on pp. 36, 38).
30. A. Bondy and U. S. R. Murty. Graph Theory (Graduate Texts in Mathematics). Springer, 2008 (cit. on p. 36).
31. J. A. Bondy. “A graph reconstructor’s manual”. In: Surveys in Combinatorics. Ed. by A. D. Keedwell. Cambridge University Press, 1991, pp. 221-252 (cit. on pp. 123, 156).
32. J. A. Bondy and R. L. Hemminger. “Graph reconstruction—a survey”. In: J. Graph Theory 1 (1977), pp. 227-268 (cit. on pp. 123, 137, 139).
33. I. Z. Bouwer. “An edge but not vertex transitive cubic graph”. In: Canad. Math. Bull. 11.4 (1968), pp. 533-534 (cit. on p. 20).
34. I. Z. Bouwer. “Vertex and edge transitive but not 1-transitive graphs”. In: Canad. Math. Bull. 13 (1970), pp. 231-237 (cit. on p. 48).
35. I. Z. Bouwer. “Section graphs for finite permutation groups”. In: J. Combin. Theory 6 (1971), pp. 378-386 (cit. on p. 62).
36. D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. Prentice Hall, 1994 (cit. on pp. 13, 17).
37. A. Bowler, P. A. Brown, and T. Fenner. “Families of pairs of graphs with a large number of common cards”. In: J. Graph Theory 63.2 (2010), pp. 146-163 (cit. on p. 144).
38. A. Bowler, P. A. Brown, T. Fenner, and W. Myrvold. “Recognizing connectedness from vertex-deleted subgraphs”. In: J. Graph Theory 67.4 (2011), pp. 285-299 (cit. on p. 144).
39. A. E. Brouwer. Parameters of Strongly Regular Graphs. www.win.tue.nl/~aeb/graphs/srg/srgtab.html (cit. on pp. 76, 77).
40. A. E. Brouwer, A. M. Cohen, and A. Neumaier. Distance-Regular Graphs. Springer-Verlag, 1989 (cit. on p. 38).
41. P. A. Brown. “On the Maximum Number of Common Cards between Various Classes of Graphs”. PhD thesis. Birkbeck College, University of London, 2008 (cit. on p. 144).
42. J. M. Burns and B. Goldsmith. “The trace of an abelian group—an application to digraphs”. In: Proc. Roy. Irish. Acad. Sect. A 95 (1995), pp. 75-79 (cit. on p. 62).
43. P. J. Cameron. “Strongly regular graphs”. In: Selected Topics in Graph Theory. Ed. by L. W. Beineke and R. J. Wilson. Academic Press, 1978. Chap. 12 (cit. on p. 77).
44. P. J. Cameron. “Automorphism groups of graphs”. In: Selected Topics in Graph Theory, Vol. 2. Ed. by L. W. Beineke and R. J. Wilson. Academic Press, 1983. Chap. 4 (cit. on p. 77).
45. P. J. Cameron. Oligomorphic Permutation Groups. Cambridge University Press, 1990 (cit. on p. 63).
46. P. J. Cameron. “Some open problems on permutation groups”. In: Groups, Combinatorics and Geometry. Ed. by M. W. Liebeck and J. Saxl. London Mathematical Society Lecture Notes 165. Cambridge University Press, 1992 (cit. on p. 169).
47. P. J. Cameron. “Stories from the age of reconstruction”. In: Congr. Num. 113 (1996), pp. 31-41 (cit. on p. 169).
48. P. J. Cameron. “Oligomorphic groups and homogeneous graphs”. In: Graph Symmetry: Algebraic Methods and Its Applications. Ed. by G. Hahn and G. Sabidussi. Kluwer Acad. Publ., 1997, pp. 23-74 (cit. on p. 63).
49. P. J. Cameron. Permutation Groups. Vol. 45. London Mathematical Society Student Texts. Cambridge University Press, 1999 (cit. on pp. 7, 17, 38, 63, 77).
50. P. J. Cameron and J. H. van Lint. Designs, Graphs, Codes and Their Links. Vol. 22. London Mathematical Society Student Texts. Cambridge University Press, 1991 (cit. on p. 77).
51. M. Capobianco and J. C. Molluzzo. Examples and Counterexamples in Graph Theory. North-Holland, 1978 (cit. on p. 122).
52. K. M. Cattermole. “Graph theory and connection networks”. In: Applications of Graph Theory. Ed. by R. J. Wilson and L. W. Beineke. Academic Press, 1979, pp. 17-57 (cit. on p. 97).
53. P. V. Ceccherini and A. Sappa. “A new characterization of hypercubes”. In: Ann. Discrete Math. 30 (1986), pp. 137-142 (cit. on p. 38).
54. G. Chartrand, A. Kaugars, and D. R. Lick. “Critically n-connected graphs”. In: Proc. Amer. Math. Soc. 32 (1972), pp. 63-68 (cit. on p. 139).
55. P. Z. Chinn. “A graph with p points and enough distinct (p — 2)-order sub graphs is reconstructible”. In: Recent Trends in Graph Theory. Ed. by M. Capobianco et al. Vol. 186. Lecture Notes in Mathematics. Springer-Verlag, 1971, pp. 71-73 (cit. on p. 139).
56. M. Conder, A. Malnic, D. Marusic, T. Pisanski, and P. Potocnik. “The edge-transitive but not vertex-transitive cubic graph on 112 vertices”. In: J. Graph Theory 50.1 (2005), pp. 25-42 (cit. on p. 38).
57. H. S. M. Coxeter, R. Frucht, and D. L. Powers. Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups. Academic Press, 1981 (cit. on pp. 91, 122).
58. D. M. Cvetkovic, M. Doob, and H. Sachs. Spectra of Graphs (3rd Ed.) Johann Ambrosius Barth, 1995 (cit. on p. 38).
59. D. Cvetkovic and M. Lepovic. “Seeking counterexamples to the reconstruction conjecture for the characteristic polynomial of graphs and a positive result”. In: Bull. Cl. Sci. Math. Nat. Sci. Math. 23 (1998), pp. 91-100 (cit. on p. 148).
60. E. R. van Dam. “Nonregular graphs with three eigenvalues”. In: J. Combin. Theory Ser. B 73.2 (1998), pp. 101-118 (cit. on p. 73).
61. R. Diestel. Graph Theory. Springer-Verlag, 1997 (cit. on p. 17).
62. J. D. Dixon and B. Mortimer. Permutation Groups. Springer-Verlag, 1996 (cit. on pp. 7, 17).
63. W. Dörfler. “Every regular graph is a quasigroup graph”. In: Discrete Math. 10 (1974), pp. 181-183 (cit. on p. 122).
64. P. Doyle. “A 27-vertex graph that is vertex-transitive and edge-transitive but not 1-transitive”. In: URL: http://arxiv.org/abs/math/070386K 1998 (cit. on p. 48).
65. P. Dulio and V. Pannone. “The converse of Kelly’s Lemma and control-classes in graph reconstruction”. In: Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 44 (2005), pp. 25-38 (cit. on pp. 129, 139).
66. B. Elspas and J. Turner. “Graphs with circulant adjacency matrices”. In: J. Com-bin. Theory 9 (1970), pp. 297-307 (cit. on p. 122).
67. P. Erdos, C. Ko, and R. Rado. “Intersection theorems for systems of finite sets”. In: Quart. J. Math. 12 (1961), pp. 313-320 (cit. on p. 122).
68. P. Erdos, A. Renyi, and V. T. Sos. “On a problem of graph theory”. In: Studia Sci. Math. Hungar. 1 (1966), pp. 215-235 (cit. on p. 77).
69. G. Exoo. Miscellaneous Topics in Combinatorics. URL: http://ginger.indstate.edu/ge/COMBIN/index.html (cit. on pp. 78, 87).
70. H. Fan. “Edge reconstruction of planar graphs with minimum degree at least three—IV”. In: Systems Sci. Math. Sci. 7 (1994), pp. 218-222 (cit. on p. 139).
71. Xin Gui Fang, Cai Heng Li, Jie Wang, and Ming Yao Xu. “On cubic Cayley graphs of finite simple groups”. In: Discrete Math. 244.1-3 (2002). Algebraic and topological methods in graph theory (Lake Bled, 1999), pp. 67-75 (cit. on p. 91).
72. I. A. Faradzev and M. Klin. “Computer package for computation with coherent configurations”. In: Proc. ISSAC-91. (Bonn). ACM Press, 1991, pp. 219-223 (cit. on p. 77).
73. S. Fiorini. “A theorem on planar graphs with an application to the reconstruction problem, I”. In: Quart. J. Math. Oxford (2) 29 (1978), pp. 353-361 (cit. on p. 134).
74. S. Fiorini. “On the edge-reconstruction of planar graphs”. In: Math. Proc. Camb. Phil. Soc. 83 (1978) (cit. on p. 139).
75. S. Fiorini and J. Lauri. “The reconstruction of maximal planar graphs. I. Recognition”. In: J. Combin. Theory Ser. B 30.2 (1981), pp. 188-195 (cit. on p. 135).
76. S. Fiorini and B. Manvel. “A theorem on planar graphs with an application to the reconstruction problem. II”. In: J. Combin. Inform. System Sci. 3.4 (1978), pp. 200-216 (cit. on p. 135).
77. J. Folkman. “Regular line-symmetric graphs”. In: J. Combin. Theory 3 (1967), pp. 215-232 (cit. on pp. 20, 35).
78. R. Frucht. “Graphs of degree three with a given abstract group”. In: Canad. J. Math. 1 (1949), pp. 365-378 (cit. on p. 62).
79. R. Frucht. “How to describe a graph”. In: Ann. N. Y Acad. Sci. 175 (1970), pp. 159-67 (cit. on p. 122).
80. R. Frucht, J. E. Graver, and M. E. Watkins. “The groups of generalized Petersen graphs”. In: Proc. Cambridge Phil. Soc. 70 (1971), pp. 211-218 (cit. on pp. 110, 122).
81. G. Gamble and C. E. Praeger. “Vertex-primitive groups and graphs of order twice the product of two distinct odd primes”. In: J. Group Theory 3.3 (2000), pp. 247-269 (cit. on p. 62).
82. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979 (cit. on pp. 13, 17).
83. G. Gauyacq. “Routages uniformes dans les graphes sommet-transitifs”. These. Univ. Bordeaux I, 1995 (cit. on p. 117).
84. G. Gauyacq. “On quasi-Cayley graphs”. In: Discrete Appl. Math. 77 (1997), pp. 43-58 (cit. on p. 117).
85. C. D. Godsil. “More odd graph theory”. In: Discrete Math. 32 (1980), pp. 205-207 (cit. on p. 122).
86. C. D. Godsil. “Neighborhoods of transitive graphs and GRRs”. In: J. Combin. Theory (Ser. B) 29 (1980), pp. 116-140 (cit. on p. 91).
87. C. D. Godsil. “The automorphism groups of some cubic Cayley graphs”. In: European J. Combin. 4.1 (1983), pp. 25-32 (cit. on p. 91).
88. C. D. Godsil and W. L. Kocay. “Constructing graphs with pairs of pseudosimilar vertices”. In: J. Combin. Theory (Ser. B) 32 (1982), pp. 146-155 (cit. on p. 91).
89. C. D. Godsil and B. D. McKay. “Spectral conditions for the reconstructibility of a graph”. In: J. Combin. Theory (Ser. B) 30 (1981), pp. 285-289 (cit. on p. 148).
90. C. Godsil and G. Royle. Algebraic Graph Theory. Springer-Verlag, 2001 (cit. on p. 17).
91. D. L. Greenwell. “Reconstructing graphs”. In: Proc. Amer. Math. Soc. 30 (1971), pp. 431-433 (cit. on p. 139).
92. D. L. Greenwell and R. L. Hemminger. “Reconstructing graphs”. In: The Many Facets of Graph Theory. Ed. by G. Chartrand and S. F. Kapoor. Vol. 110. Lecture Notes in Mathematics. (Proc. of the conference held at Western Michigan University Kalamazoo Mich., 1968). Springer-Verlag, 1969, pp. 91-114 (cit. on p. 139).
93. M. Gromov. “Groups of polynomial growth and expanding maps”. In: Inst. Hautes Etudes Sci. Publ. Math. 53 (1981), pp. 53-73 (cit. on p. 63).
94. G. Hahn and G. Sabidussi (Eds.) Graph Symmetry: Algebraic Methods and Applications. Kluwer Acad. Publ., 1997 (cit. on p. 17).
95. G. Hahn and C. Tardif. “Homomorphisms of graphs”. In: Graph Symmetry: Algebraic Methods andApplications. Ed. by G. Hahn and G. Sabidussi. Kluwer Acad. Publ., 1997, pp. 107-166 (cit. on p. 108).
96. R. Hammack, W. Imrich, and S. KlavZar. Handbook of Product Graphs, Second Edition. Discrete Mathematics and Its Applications. Taylor & Francis, 2011 (cit. on p. 108).
97. F. Harary. Graph Theory. Addison-Wesley, 1969 (cit. on p. 17).
98. F. Harary and J. Lauri. “The class-reconstruction number of maximal planar graphs”. In: Graphs and Combinatorics 3 (1987), pp. 45-53 (cit. on pp. 144, 147).
99. F. Harary and J. Lauri. “On the class-reconstruction number of trees”. In: Quart. J. Math. Oxford (2) 39 (1988), pp. 47-60 (cit. on pp. 144, 147).
100. F. Harary and E. M. Palmer. “A note on similar points and similar lines in a graph”. In: Rev. Roum. Math. Pures et Appl 10 (1965), pp. 1489-1492(cit. on p. 91).
101. F. Harary and E. M. Palmer. “On similar points of a graph”. In: J. Math. Mech. 15 (1966), pp. 623-630 (cit. on p. 91).
102. F. Harary and E. M. Palmer. “On the problem of reconstructing a tournament from subtournaments”. In: Monatsh. Math. 71 (1967), pp. 14-23 (cit. on p. 136).
103. F. Harary and E. M. Palmer. Graphical Enumeration. Academic Press, 1973 (cit. on pp. 10, 36, 38).
104. F. Harary, A. Vince, and D. Worley. “A point-symmetric graph that is nowhere reversible”. In: Siam J. Alg. Disc. Meth. 3.3 (1982), pp. 285-287 (cit. on p. 91).
105. D. Hetzel. “Über reguläre graphische Darstellungen von auflösbaren Gruppen”. Diplomarbeit. Technische Universitat Berlin, 1976 (cit. on p. 91).
106. C. M. Hoffman. “Subcomplete generalisations of graph isomorphism”. In: J. Computer and System Sciences 25 (1982), pp. 332-359 (cit. on pp. 17, 63).
107. D. F. Holt. “A graph which is edge transitive but not arc transitive”. In: J. Graph Theory 5 (1981), pp. 201-204 (cit. on pp. 47, 48).
108. D. A. Holton and J. Sheehan. The Petersen Graph. Vol. 7. Australian Mathematical Society Lecture Series. Cambridge University Press, 1993 (cit. on pp. 62, 122).
109. W. Imrich. “Graphs with transitive abelian automorphism group”. In: Combinatorial Theory and Its Applications II. Ed. by P. Erdos, A. Renyi, and V. T. Sos. Vol. 4. Colloq. Math. Soc. J. Bolyai. North-Holland, 1970, pp. 651-656 (cit. on pp. 89, 91).
110. W. Imrich. “Assoziative Produkte von Graphen”. In: Osterreich Akad. Wiss. Math.-Natur Kl. S.-B. 180.2 (1972), pp. 203-239 (cit. on p. 108).
111. W. Imrich. “On graphs and regular groups”. In: J. Combin. Theory (Ser B) 19 (1975), pp. 174-180 (cit. on p. 91).
112. W. Imrich. “Graphical regular representations of groups of odd order”. In: Combinatorics. Ed. by A. Hajnal and V. T. Sos. Vol. 18. Colloq. Math. Soc. J. Bolyai. North-Holland, 1976, pp. 611-622 (cit. on p. 91).
113. W. Imrich and H. Izbichi. “Associative products of graphs”. In: Monatsh. Math. 80.4 (1975), pp. 277-281 (cit. on pp. 97, 108).
114. W. Imrich and S. KlavZar. Product Graphs: Structure and Recognition. Wiley, 2000 (cit. on p. 108).
115. W. Imrich and M. E. Watkins. “On graphical regular representations of cyclic extensions of groups”. In: Pacific J. Math. 55.2 (1974), pp. 461-477 (cit. on p. 91).
116. W. Imrich and M. E. Watkins. “On automorphism groups of Cayley graphs”. In: Periodica Mathematica Hungarica 7.3-4 (1976), pp. 243-258 (cit. on p. 91).
117. T. R. Jensen and B. Toft. Graph Coloring Problems. J. Wiley and Sons, 1995 (cit. on p. 105).
118. I. N. Kagno. “Linear graphs of degree 6 and their groups”. In: Amer. J. Math. 68 (1946), pp. 505-520 (cit. on p. 59).
119. W. Kantor. “k-Homogeneous graphs”. In: Math. Z. 124 (1972), pp. 261-265 (cit. on p. 114).
120. P. J. Kelly. “A congruence theorem for trees”. In: Pacific J. Math. 7 (1957), pp. 961-968 (cit. on p. 140).
121. R. J. Kimble, A. J. Schwenk, and P. K. Stockmeyer. “Pseudosimilar vertices in a graph”. In: J. Graph Theory 5 (1981), pp. 171-181 (cit. on p. 91).
122. D. G. Kirkpatrick, M. M. Klawe, and D. G. Corneil. “On pseudosimilarity in trees”. In: J. Combin. Theory (Ser. B) 34 (1983), pp. 323-339 (cit. on p. 91).
123. M. H. Klin and R. Poschel. “The Konig problem, the isomorphism problem for cyclic graphs and the method of Schur rings”. In: Algebraic Methods in Graph Theory. Ed. by L. Lovasz and V. T. Sos. Vol. 25. Colloq. Math. Soc. J. Bolyai. North-Holland, 1981, pp. 405-430 (cit. on p. 122).
124. M. Klin, J. Lauri, and M. Ziv-Av. “Links between two semisymmetric graphs on 112 vertices via association schemes”. In: J. Symbolic Comput. 47.10 (2012), pp. 1175-1191 (cit. on p. 38).
125. M. Klin, C. Pech, S. Reichard, A. Woldar, and M. Ziv-Av. “Examples of computer experimentation in algebraic combinatorics”. In: Ars Math. Contemp. 3 (2010), pp. 237-258 (cit. on pp. 48, 77).
126. J. Kobler, U. Schöning, and J. Toran. The Graph Isomorphism Problem: Its Structural Complexity. Birkhauser, 1993 (cit. on pp. 14, 17, 139).
127. W. L. Kocay. “On reconstructing spanning subgraphs”. In: Ars Combinatoria 11 (1981), pp. 301-313 (cit. on p. 156).
128. W. L. Kocay. “Some new methods in reconstruction theory”. In: Combinatorial Mathematics IX. Ed. by E. J. Billington, S. Oates-Williams, and A. Penfold Street. Vol. 952. Lecture Notes in Mathematics. (Proc. 9th Australian Conf. on Combinatorial Mathematics, Univ. of Queensland, Brisbane). Springer-Verlag, 1982, pp. 89-114 (cit. on p. 156).
129. W. L. Kocay. “Attaching graphs to pseudosimilar vertices”. In: J. Austral. Math. Soc. (Ser. A) 36 (1984), pp. 53-58 (cit. on p. 91).
130. W. L. Kocay. “On Stockmeyer’s non-reconstructible tournaments”. In: J. Graph Theory 9 (1985), pp. 473-476 (cit. on p. 137).
131. W. L. Kocay. “Graphs & groups, aMacintosh application for graph theory”. In: J. Combin. Maths. and Combin. Comput. 3 (1988), pp. 195-206 (cit. on pp. 14, 17, 63, 139).
132. A. D. Korshunov. “Number of nonisomorphic graphs in an n-point graph”. In: Math. Notes of the Acad. USSR 9 (1971), pp. 155-160 (cit. on p. 38).
133. I. Krasikov, A. Lev, and B. D. Thatte. “Upper bounds on the automorphism group of a graph”. In: Discrete Math. 256.1-2 (2002), pp. 489-493 (cit. on p. 169).
134. D. Kratsch and L. A. Henaspaandra. “On the complexity of graph reconstruction”. In: Math. Systems Theory 27.3 (1994), pp. 257-273 (cit. on p. 139).
135. V. Krishnamoorthy and K. R. Parthasarathy. “Cospectral graphs and digraphs with given automorphism group”. In: J. Combin. Theory (Ser B) 19 (1975), pp. 204-213 (cit. on p. 91).
136. J. Lauri. “The reconstruction of maximal planar graphs, II: Reconstruction”. In: J. Combin. Theory (Ser. B.) 30 (1981), pp. 196-214 (cit. on pp. 136, 139).
137. J. Lauri. “Endvertex-deleted subgraphs”. In: Ars Combinatoria 36 (1993), pp. 171-182 (cit. on pp. 91, 169).
138. J. Lauri. “Pseudosimilarity in graphs—A survey”. In: Ars Combinatoria 36 (1997), pp. 171-182 (cit. on p. 91).
139. J. Lauri. “Constructing graphs with several pseudosimilar vertices or edges”. In: Discrete Math. 267.1-3 (2003). Combinatorics 2000 (Gaeta), pp. 197-211 (cit. on p. 91).
140. J. Lauri. “The Reconstruction Problem”. In: Handbook of Graph Theory. Ed. by J. L. Gross, J. Yellen, and P. Zhang. Discrete Mathematics and Its Applications. 2014 (cit. on p. 123).
141. J. Lauri, R. Mizzi, and R. Scapellato. “Two-fold orbital digraphs and other constructions.” In: International J. of Pure and Applied Math. 1 (2004), pp. 63-93 (cit. on p. 108).
142. J. Lauri, R. Mizzi, and R. Scapellato. “Two-fold automorphisms of graphs.” In: Australasian J. Combinatorics. 49 (2011), pp. 165-176 (cit. on p. 108).
143. J. Lauri, R. Mizzi, and R. Scapellato. “A generalisation of isomorphisms with applications.” Preprint. 2014 (cit. on pp. 103, 104, 108).
144. J. Lauri, R. Mizzi, and R. Scapellato. “A smallest unstable asymmetric graph and an infinite family of asymmetric graphs with arbitrarily large instability index”. Preprint. 2015 (cit. on p. 108).
145. J. Lauri, R. Mizzi, and R. Scapellato. “Unstable graphs: A fresh outlook via TF-automorphisms”. In: Ars Mathematica Contemporanea 8.1 (2015), pp. 115-131 (cit. on p. 108).
146. J. Lauri and R. Scapellato. “A note on graphs all of whose edges are pseudosimilar”. In: Graph Theory Notes of New York 21 (1996), pp. 11-13 (cit. on p. 91).
147. W. Lederman and A. J. Weir. Introduction to Group Theory (2nd Ed.) Longman, 1996 (cit. on pp. 7, 17).
148. Cai Heng Li. “The solution of a problem of Godsil on cubic Cayley graphs”. In: J. Combin. Theory Ser. B 72.1 (1998), pp. 140-142 (cit. on p. 91).
149. D. Livingstone and A. Wagner. “Transitivity of finite permutation groups”. In: Math. Z. 90 (1965), pp. 393-403 (cit. on pp. 114, 115).
150. L. Lovasz. “Unsolved problem II”. In: Combinatorial Structures and Their Applications. Ed. by R. Guy, H. Hanani, N. Sauer, and J. Schonheim. Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications, 1969. Gordan and Breach, 1970 (cit. on p. 62).
151. L. Lovasz. “A note on the line reconstruction problem”. In: J. Combin. Theory (Ser B) 13 (1972), pp. 309-310 (cit. on p. 169).
152. L. Lovasz. “Some problems of graph theory”. In: Matematikus Kurir (1983) (cit. on p. 169).
153. L. Lovasz. Combinatorial Problems and Exercises. Second ed. North-Holland Publishing Co., Amsterdam, 1993 (cit. on p. 138).
154. M. Lovrecic-Sarazin. “A note on the generalized Petersen graphs that are also Cayley graphs”. In: J. Comb. Theory (Ser. B) 69 (1997), pp. 189-192 (cit. on pp. 111, 122).
155. E. M. Luks. “Isomorphism of graphs of bounded valence can be tested in polynomial time”. In: J. Computer and System Sciences 25 (1982), pp. 42-65 (cit. on p. 17).
156. M. Macaj and J. Siran. “Search for properties of the missing Moore graph”. In: Linear Alg. and Applics. 432 (2010), pp. 2381-2389 (cit. on p. 77).
157. D. Macpherson. “The action of an infinite permutation group on the unordered subsets of a set”. In: Proc. London Math. Soc. 46.3 (1983), pp. 471-486 (cit. on p. 63).
158. D. Macpherson. “Growth rates in infinite graphs and permutation groups”. In: Proc. London Math. Soc. 51.3 (1985), pp. 285-294 (cit. on p. 63).
159. W. Magnus, A. Karrass, and D. Solitar. Combinatorial group theory. Second ed. Presentations of groups in terms of generators and relations. Dover Publications, 2004 (cit. on p. 7).
160. A. Malnic, D. Marusic, P. Potocnik, and C. Wang. “An infinite family of cubic edge- but not vertex-transitive graphs”. In: Discrete Math. 280.1-3 (2004), pp. 133-148 (cit. on p. 20).
161. B. Manvel. “Reconstruction of trees”. In: Canadian J. Math. 22 (1970), pp. 55-60 (cit. on p. 148).
162. B. Manvel. “On reconstructing graphs from their sets of subgraphs”. In: J. Com-bin. Theory (Ser. B) 21 (1976), pp. 156-165 (cit. on pp. 139, 148).
163. D. Marusic. “Cayley properties of vertex symmetric graphs”. In: Ars Combin. 16B (1983), pp. 297-302 (cit. on p. 62).
164. D. Marusic. “Hamiltonian circuits in Cayley graphs”. In: Discrete Math. 46 (1983), pp. 49-54 (cit. on p. 62).
165. D. Marusic. “On vertex-transitive graphs of order qp”. In: J. Combin. Math. Combin. Comput. 4 (1988), pp. 97-114 (cit. on p. 116).
166. D. Marusic and T. Pisanski. “The Gray graph revisited”. In: J. Graph Theory 35.1 (2000), pp. 1-7 (cit. on p. 21).
167. D. Marusic and R. Scapellato. “A class of non-Cayley vertex-transitive graphs associated with PSL(2, p)”. In: Discrete Math. 109 (1992), pp. 161-170 (cit. on p. 122).
168. D. Marusic and R. Scapellato. “Characterizing vertex-transitive pq-graphs with an imprimitive automorphism subgroup”. In: J. Graph Theory 16 (1992), pp. 375-387 (cit. on p. 122).
169. k)”. In: J. Combin. Theory (Ser B) 58 (1993), pp. 46-57 (cit. on pp. 116, 122).
170. 2) on cosets of PGL(2, q)”. In: Discrete Math. 134 (1994), pp. 99-110 (cit. on p. 122).
171. D. Marusic; and R. Scapellato. “Classification of vertex-transitivepq-digraphs”. In: Atti 1st. Lombardo (Rend. Sci.) A-128.1 (1994), pp. 31-36 (cit. on p. 122).
172. D. Marusic and R. Scapellato. “Classifying vertex-transitive graphs whose order is a product of two primes”. In: Combinatorica 14.2 (1994), pp. 187-201 (cit. on p. 122).
173. D. Marusic and R. Scapellato. “Permutation groups with conjugacy complete stabilizer”. In: Discrete Math. 134 (1994), pp. 93-98 (cit. on p. 122).
174. D. Marusic and R. Scapellato. “Permutation groups, vertex-transitive digraphs and semi-regular automorphisms”. In: Europ. J. Combinatorics 19 (1998), pp. 707-712 (cit. on p. 115).
175. D. Marusic, R. Scapellato, and N. Zagaglia Salvi. “A characterization of particular symmetric (0,1) matrices”. In: Linear Algebra Appl. 119 (1989), pp. 153-162 (cit. on pp. 102, 108).
176. D. Marusic, R. Scapellato, and N. Zagaglia Salvi. “Generalized Cayley graphs”. In: Discrete Math. 102. 3 (1992). URL: http://dx.doi.org/10.1016/0012-365X(92)90121-U, pp. 279-285 (cit. on pp. 103, 108, 119, 120).
177. D. Marusic, R. Scapellato, and B. Zgrablic. “On quasiprimitive pqr-graphs.” In: Algebra Colloq. 2.4 (1995), pp. 295-314 (cit. on p. 116).
178. P. Maynard. “On Orbit Reconstruction Problems”. PhD thesis. UEA, Norwich, 1996 (cit. on p. 169).
179. P. Maynard and J. Siemons. “On the reconstruction index of permutation groups: semiregular groups”. In: Aequationes Math. 64.3 (2002), pp. 218-231 (cit. on p. 169).
180. P. Maynard and J. Siemons. “On the reconstruction index of permutation groups: general bounds”. In: Aequationes Math. 70.3 (2005), pp. 225-239 (cit. on p. 169)
181. B. D. McKay and A. Piperno. “Practical graph isomorphism, {II}”. In: Journal of Symbolic Computation 60 (2014). URL: www.sciencedirect.com/science/article/pii/S0747717113001193, pp. 94-112 (cit. on pp. 15, 17).
182. B. D. McKay and C. E. Praeger. “Vertex-transitive graphs that are not Cayley graphs I”. In: J. Austral. Math. Soc. (Ser. A) 56 (1994), pp. 53-63 (cit. on p. 62).
183. B. D. McKay and C. E. Praeger. “Vertex-transitive graphs that are not Cayley graphs II”. In: J. Graph Theory 22.4 (1996), pp. 321-324 (cit. on p. 62).
184. J. Meier. Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups. Vol. 73. London Mathematical Society Student Texts. Cambridge, 2008 (cit. on p. 63).
185. J. Meng and M. Xu. “Automorphisms of groups and isomorphisms of Cayley digraphs”. In: Australasian J. Combin. 12 (1995), pp. 93-100 (cit. on p. 91).
186. J. Milnor. “A note on curvature and finite groups”. In: J. Diff. Geom. 2 (1968), pp. 1-7 (cit. on p. 63).
187. J. Milnor. “Growth of finitely generated solvable groups”. In: J. Diff. Geom. 2 (1968), pp. 447-449 (cit. on p. 63).
188. V. B. Mnukhin. “Reconstruction of k-orbits of a permutation group”. In: Math. Notes 42 (1987), pp. 975-980 (cit. on p. 169).
189. V. B. Mnukhin. “The k-orbit reconstruction and the orbit algebra”. In: Acta Applic. Math. 29 (1992), pp. 83-117 (cit. on p. 169).
190. V. B. Mnukhin. “The reconstruction of oriented necklaces”. In: J. Combin., Inf. & Sys. Sciences 20.1-4 (1995), pp. 261-272 (cit. on p. 169).
191. V. B. Mnukhin. “The k-orbit reconstruction for abelian and Hamiltonian groups”. In: Acta Applic. Math. 52 (1998), pp. 149-162 (cit. on p. 169).
192. R. Molina. “Correction of a proof on the ally-reconstruction number of a disconnected graph. Correction to: “The ally-reconstruction number of a disconnected graph” [Ars Combin. 28 (1989), 123-127; MR1039138 (90m:05094)] by W. J. Myrvold”. In: Ars Combin. 40 (1995), pp. 59-64 (cit. on p. 143).
193. R. Molina. “The edge reconstruction number of a disconnected graph”. In: J. Graph Theory 19.3 (1995), pp. 375-384 (cit. on p. 143).
194. A. Mowshowitz. “The group of a graph whose adjacency matrix has all distinct eigenvalues”. In: Proof Techniques in Graph Theory. Ed. by F. Harary. Academic Press, 1969, pp. 109-110(cit. on p. 38).
195. A. Mowshowitz. “The adjacency matrix and the group of a graph”. In: New Directions in the Theory of Graphs. Ed. by F. Harary. Academic Press, 1973 (cit. on p. 38).
196. V. Müller. “Probabilistic reconstruction from subgraphs”. In: Comment. Math. Univ. Carolinae 17 (1976), pp. 709-719 (cit. on pp. 38, 169).
197. M. Muzychuk. “¿Adam’s conjecture is true in the square-free case”. In: J. Combin. Theory (Ser. A) 72 (1995), pp. 118-134 (cit. on p. 122).
198. M. Muzychuk. “On ¿Adam’s conjecture for circulant graphs”. In: Discrete Math. 176 (1997), pp. 285-298 (cit. on p. 122).
199. M. Muzychuk and M. Klin. “On graphs with three eigenvalues”. In: Discrete Math. 189.1-3 (1998), pp. 191-207 (cit. on p. 73).
200. W. Myrvold. “Ally and Adversary Reconstruction Problems”. PhD thesis. University of Waterloo, Ontario, Canada, 1988 (cit. on pp. 142, 144, 148).
201. W. J. Myrvold. “The ally-reconstruction number of a disconnected graph”. In: Ars Combin. 28 (1989), pp. 123-127 (cit. on p. 143).
202. W. J. Myrvold. “The ally-reconstruction number of a tree with five or more vertices is three”. In: J. Graph Theory 14 (1990), pp. 149-166 (cit. on pp. 144, 147).
203. C. St. J. A. Nash-Williams. “The reconstruction problem”. In: Selected Topics in Graph Theory. Ed. by L. W. Beineke and R. J. Wilson. Academic Press, 1978. Chap. 8 (cit. on pp. 123, 169).
204. R. Nedela and M. Škoviera. “Which generalized Petersen graphs are Cayley graphs?” In: J. Graph Theory 19 (1995), pp. 1-11 (cit. on pp. 111, 122).
205. E. D. Nering. Linear Algebra and Matrix Theory. John Wiley & Sons, 1970 (cit. on p. 77).
206. J. Nesestril and V. Rodl. “Products of graphs and their applications”. In: Lecture Notes in Mathematics 1018. Ed. by J. W. Kennedy, M. Borowiechki and M. M. Syslo. Springer-Verlag, 1983, pp. 151-160 (cit. on p. 105).
207. R. J. Nowakawski and D. F. Hall. “Associative products and their independence, domination and coloring numbers”. In: Discuss. Math. Graph Theory 16.1 (1996), pp. 53-79 (cit. on p. 108).
208. L. A. Nowitz and M. E. Watkins. “Graphical regular representations of non-abelian groups, I”. In: Canadian J. Math 26.6 (1972), pp. 993-1008 (cit. on p. 91).
209. L. A. Nowitz and M. E. Watkins. “Graphical regular representations of non-abelian groups, II”. In: Canadian J. Math 26.6 (1972), pp. 1009-1018 (cit. on p. 91).
210. V. Nydl. “Some results concerning reconstruction conjecture”. In: Proceedings of the 12th winter school on abstract analysis (Srnl, 1984). Suppl. 6. 1984, pp. 243-246 (cit. on p. 138).
211. V. Nydl. “A note on reconstructing of finite trees from small subtrees”. In: Acta Univ. Carolin. Math. Phys. 31.2 (1990). 18th Winter School on Abstract Analysis (Srni, 1990), pp. 71-74 (cit. on p. 138).
212. O. Ore. Theory of Graphs. American Mathematical Society, 1962 (cit. on p. 94).
213. W. Pacco and R. Scapellato. “Digraphs having the same canonical double covering”. In: Discrete Math. 173 (1997), pp. 291-296 (cit. on pp. 106, 108).
214. M. Petersdorf and H. Sachs. “Spectrum und Automorphismengruppe eines Graphen”. In: Combinatorial Theory and Its Applications. Vol. III. North-Holland, 1969, pp. 891-907 (cit. on p. 38).
215. L. Porcu. “Sul raddoppio di un grafo”. In: Att. Ist. Lombardo (Rend. Sci.) A.110 (1976), pp. 353-360 (cit. on p. 108).
216. M. Pouzet. “Application de la notion de relation presquenchaînable au dnombrement des restrictions finies d’une relation”. In: Z. Math. Logik Grundl. Math. 27 (1981), pp. 289-332 (cit. on p. 63).
217. L. Pyber. “The edge-reconstruction of Hamiltonian graphs”. In: J. Graph Theory 14 (1990), pp. 173-179 (cit. on p. 169).
218. n”. In: J. Combin. Theory (Ser A) 83.2 (1998), pp. 169-187 (cit. on p. 169).
219. A. J. Radcliffe and A. D. Scott. “Reconstructing subsets of reals”. In: Electron. J. Combin. 1 (1999), Research Paper 20 (cit. on p. 169).
220. S. Ramachandran. “N-reconstructibility of nonreconstructible digraphs”. In: Discrete Math. 46.3 (1983), pp. 279-294 (cit. on p. 137).
221. S. Ramachandran. “Reconstruction number for Ulam’s conjecture”. In: Ars Combin. 78 (2006), pp. 289-296 (cit. on p. 144).
222. J. J. Rotman. An Introduction to the Theory of Groups (4th Ed.) SpringerVerlag, 1995 (cit. on pp. 7, 17).
223. G. Sabidussi. “On the minimum order of graphs with a given automorphism group”. In: Monatsh. Math. 63 (1959), pp. 124-127 (cit. on p. 62).
224. G. Sabidussi. “Graph multiplication”. In: Math. Z. 72 (1960), pp. 446-457 (cit. on p. 108).
225. G. Sabidussi. “Vertex transitive graphs”. In: Monat. Math. 68 (1964), pp. 426-438 (cit. on p. 122).
226. H. Sachs. “Uber Teiler, Faktoren und characterische Polynome von Graphen II”. In: Wiss. Z. Techn. Hosch. Ilmenau 13 (1967), pp. 405-412 (cit. on p. 77).
227. W. A. Stein et al. Sage Mathematics Software (Version 6.3). www.sagemath.org. The Sage Development Team. 2014 (cit. on p. 15).
228. R. Scapellato. “On F-geodetic graphs”. In: Discrete Math. 80 (1990), pp. 313-325 (cit. on p. 38).
229. R. Scapellato. “A characterization of bipartite graphs associated with BIB-designswith X = 1”. In: Discrete Math. 112 (1993), pp. 283-287 (cit. on p. 38).
230. R. Scapellato. “Vertex-transitive graphs and digraphs”. In: Graph Symmetry: Algebraic Methods and Applications. Ed. by G. Hahn and G. Sabidussi. Kluwer Acad. Publ., 1997, pp. 319-378 (cit. on pp. 106, 116, 122).
231. A. J. Schwenk. “Spectral reconstruction problems”. In: Topics in Graph Theory. Ed. by F. Harary. Vol. 328. Annals New York Academy of Sciences. New York Academy of Sciences, 1979, pp. 183-189 (cit. on p. 148).
232. I. Sciriha. “Polynomial reconstruction and terminal vertices”. In: Linear Algebra Appl. 356 (2002). Special issue on algebraic graph theory (Edinburgh, 2001), pp. 145-156 (cit. on p. 148).
233. A. Seress. “On vertex-transitive, non-Cayley graphs of order pqr”. In: Discrete Math. 182 (1998), pp. 279-292 (cit. on p. 62).
234. Y. Shibata and Y. Kikuchi. “Graph products based on distance in graphs”. In: IEICE Trans. Fundamentals E83-A.3 (2000), pp. 459-464 (cit. on p. 108).
235. L. H. Soicher. “GRAPE: a system for computing with graphs and groups”. In: Groups and Computation. Ed. by L. Finkelstein and W.M. Kantor. Vol. 11. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1993, pp. 287-291 (cit. on pp. 15, 17).
236. T. Spence. Strongly Regular Graphs on at Most 64 Vertices. URL: www.maths.glaac.uk/~es/srgraphs.php (cit. on p. 78).
237. P. K. Stockmeyer. “The falsity of the reconstruction conjecture for tournaments”. In: J. Graph Theory 1 (1977), pp. 19-25 (cit. on p. 137).
238. P. K. Stockmeyer. “Tilting at windmills or my quest for non-recon structible graphs”. In: Congressus Numerantium 63 (1988), pp. 188-200 (cit. on p. 137).
239. D. B. Surowski. “Stability of arc-transitive graphs”. In: J. Graph Theory 38.2 (2001), pp. 95-110 (cit. on p. 108).
240. D. B. Surowski. “Unexpected symmetries in unstable graphs”. In: J. Graph Theory 38 (2001), pp. 95-110 (cit. on p. 108).
241. D. B. Surowski. “Automorphism groups of certain unstable graphs”. In: Math. Slovaca 53.3 (2003), pp. 215-232 (cit. on p. 108).
242. R. G. Swan. “A simple proof of Rankin’s campanological theorem”. In: Amer. Math. Monthly 106 (1999), pp. 159-161 (cit. on p. 62).
243. The GAP Group. GAP—Groups, Algorithms and Programming, Version 4.1. www-gap.dcs.st-and.ac.uk/gap: Aachen, St. Andrews, 1999 (cit. on pp. 15, 17).
244. R. M. Thomas. “Cayley graphs and group representations”. In: Math. Proc. Camb. Philos. Soc. 103 (1988), pp. 385-387 (cit. on p. 62).
245. C. Thomassen. “A characterisation of locally finite vertex-transitive graphs”. In: J. Combin. Theory (Ser. B) 43 (1987), pp. 116-119 (cit. on p. 91).
246. V. I. Trofimov. “Graphs with polynomial growth”. In: Math. USSR Sbornik. 59 (1985), pp. 405-417 (cit. on p. 63).
247. V. I. Trofimov. “On the action of a group on a graph”. In: Acta. Appl. Math. 29 (1992), pp. 161-170 (cit. on p. 63).
248. J. Turner. “Point-symmetric graphs with a prime number of points”. In: J. Combin. Theory 3 (1967), pp. 136-145 (cit. on p. 122).
249. W. T. Tutte. “A family of cubical graphs”. In: Proc. Cambridge Philos. Soc. 43 (1947), pp. 26-40 (cit. on p. 38).
250. W. T. Tutte. Connectivity in Graphs. Toronto University Press, 1966 (cit. on p. 38).
251. W. T. Tutte. “All the king’s horses—a guide to reconstruction”. In: Graph Theory and Related Topics. Ed. by J. A. Bondy and U. S. R. Murty. Academic Press, 1979 (cit. on p. 156).
252. J. H. van Lint and R. M. Wilson. A Course in Combinatorics. Cambridge University Press, 2001 (cit. on p. 148).
253. M. E. Watkins. “Connectivity of transitive graphs”. In: J. Combin. Theory 8 (1970), pp. 23-29 (cit. on p. 60).
254. M. E. Watkins. “Ends and automorphisms of infinite graphs”. In: Graph Symmetry: Algebraic Methods and Its Applications. Ed. by G. Hahn and G. Sabidussi. Kluwer Acad. Publ., 1997, pp. 379-414 (cit. on pp. 63, 77).
255. R. Weiss. “The non-existence of 8-transitive graphs”. In: Combinatorica 1 (1983), pp. 309-311 (cit. on p. 38).
256. M. Welhan. “Reconstructing trees from two cards”. In: J. Graph Theory 63 (2010), pp. 243-257 (cit. on p. 144).
257. D. B. West. Introduction to Graph Theory. Prentice-Hall, 1996 (cit. on pp. 3, 17).
258. H. Whitney. “Congruent graphs and the connectivity of graphs”. In: Amer. J. Math. 54 (1932), pp. 150-168 (cit. on pp. 12, 139).
259. R. J. Wilson. Introduction to Graph Theory. Longman, 1997 (cit. on pp. 3, 17).
260. S. Wilson. “Unexpected symmetries in unstable graphs”. In: J. Combinatorial Theory B.98 (2005), pp. 359-383 (cit. on p. 108).
261. D. Witte and J. Gallian. “A survey: Hamiltonian cycles in Cayley graphs”. In: Discrete Math. 51 (1984), pp. 293-304 (cit. on p. 62).
262. J. A. Wolf. “Growth of finitely generated solvable groups and curvature of Rie-mannian manifolds”. In: J. Diff. Geom. 2 (1968), pp. 421-446 (cit. on p. 63).
263. M. Y. Xu. “Automorphism groups and isomorphisms of Cayley digraphs”. In: Discrete Math. 182 (1998), pp. 309-319 (cit. on p. 91).
264. 5”. In: Sci. China Ser. A 47.4 (2004), pp. 593-604 (cit. on p. 91).
265. H. Yuan. “An eigenvector condition for reconstructibility”. In: J. Combin. Theory (Ser B) 32 (1982), pp. 245-256 (cit. on p. 148).
266. Y. Zhao. “On the edge reconstruction of graphs embedded in surfaces. III”. In: J. Combin. Theory (Ser. B) 74 (1998), pp. 302-310 (cit. on p. 139).
267. A. A. Zykov. Fundamentals of Graph Theory. Translated from the Russian and edited by L. Boron, C. Christenson and B. Smith. Moscow, ID: BCS Associates, 1990 (cit. on pp. 99, 108).