Pseudosimilarity in graphs - A survey

Ars Combinatoria

Volumn 46, Issue , 1997, Pages 77-95

  Lauri, Josef ^a  

^a UNIVERSITY OF MALTA   (Malta)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038913453     PISSN: 03817032     EISSN: 28175204     Source Type: Journal    
DOI: None     Document Type: Review

References (55)

1. L.D. Andersen, S. Ding, G. Sabidussi and P.D. Vestergaard, 'Edge orbits and edge-deleted subgraphs', Graphs and Combinatorics 8 (1992), 31-44.
2. L.D. Andersen, S. Ding, and P.D. Vestergaard, 'On the set edge-reconstruction conjecture', preprint (1990).
3. N.L. Biggs, Algebraic Graph Theory (Second Edition), Cambridge University Press, 1994.
4. J. Bosak, 'Induced subgraphs with the same order and size', Math. Slovaca 33 (1983), 105-119.
5. I.Z. Bouwer, 'Section graphs for finite permutation groups', J. Combin. Theory 6 (1969), 378-386.
6. P.J. Cameron, personal communication, (1991).
7. D.G. Corneil, D.G. Kirkpatrick and M.M. Klawe, 'Generalized notions of pseudo-similarity in graphs', Congressus Numerantium 28 (1980), 293-308.
8. P. Duchet, Z. Tuza and P.D. Vestergaard, 'Graphs in which all spanning subgraphs with r edges fewer are isomorphic', Congressus Numerantium 67 (1988), 45-58.
9. M.N. Ellingham, 'Vertex-switching, isomorphism, and pseudosimilarity', J. Graph Theory 15 (1991), 563-572.
10. C.D. Godsil, 'Neighbourhoods of transitive graphs and GRR's', J. Combin. Theory Ser. B., 29 (1980), 116-140.
11. C.D. Godsil, 'Problem 66', Discrete Math. 55 (1985), 336.
12. C.D. Godsil and W.L. Kocay, 'Constructing graphs with pairs of pseudo-similar vertices', J. Combin. Theory Ser. B. 32 (1982), 146-155.
13. C.D. Godsil and W.L. Kocay, 'Graphs with three mutually pseudo-similar vertices', J. Combin. Theory Ser. B 35 (1983) 240-246.
14. F. Harary, Graph Theory, Addison-Wesley, Reading, Mass. (1969).
15. F. Harary and J. Lauri, 'On the class-reconstruction number of trees', Quart. J. Math. Oxford 39 (1988), 47-60.
16. F. Harary and E.M. Palmer, 'A note on similar points and similar lines of a graph, Rev. Roumaine Math. Pres Appl. 10 (1965), 1489-1492.
17. F. Harary and E.M. Palmer, 'On similar points of a graph', J. Math. Mech. 15 (1966), 623-630.
18. F. Harary and E.M. Palmer, 'The reconstruction of a tree from its maximal subtrees', Canad. J. Math. 18 (1966), 803-810.
19. F. Harary, A. Vince and D. Worley, 'A point-symmetric graph that is nowhere reversible', Siam. J. Alg. Disc. Meth. 3 (1982), 285-287.
20. W.C. Herndon and M.L. Ellzey, 'Isospectral graphs and molecules', Tetrahedron 31 (1975), 99-107.
21. D. Hetzel, Über reguläre graphische Darstellungen von auflösbaren Gruppen, Diplomarbeity, Technische Universitat Berlin, 1976.
22. W. Imrich, 'Graphical regular representations of groups of odd order', in Combinatorics (Colloq. Math. Soc. J. Bolyai 18), A. Hajnal and V.T. Sós eds.), North-Holland (1978), 611-622.
23. M. Jean, 'Line-symmetric tournaments', in Recent Progress in Combinatorics, W.T. Tutte ed., Academic Press, New York (1969) 265-271.
24. R.J. Kimble, 'Existence of graphs where almost every edge is pseudo-similar', Theory and Applications of Graphs (Proc. 4th International Conf., Theory and Applications of Graphs, Western Michigan University, Kalamazoo, G. Chartrand et al. eds.), Wiley (1981), 431-436.
25. R.J. Kimble, A.J. Schwenk and P.K. Stockmeyer, 'Pseudosimilar vertices in a graph', J. Graph Theory 5 (1981), 171-181.
26. D.G. Kirkpatrick, M.M. Klawe and D.G. Corneil, 'On pseudosimilarity in trees, J. Combin. Theory Ser. B 34 (1983), 323-339.
27. W.L. Kocay, 'On reconstructing degree sequences', Utilitas Math. 17 (1980), 151-162.
28. W.L. Kocay, 'On pseudosimilar vertices', Ars Combinatoria 10 (1980), 147-163.
29. W.L. Kocay, 'On the number of pseudosimilar vertices in a graph', Utiltas Math. 18 (1980), 175-179.
30. W.L. Kocay, 'A necessary but insufficient condition for pseudosimilar vertices', Ars Combin. 13 (1982), 55-60.
31. W.L. Kocay, 'A small graph with three mutually pseudo-similar vertices', Ars Combin. 14 (1982), 99-103.
32. W.L. Kocay, 'Some new methods in reconstruction theory', in Combinatorial Mathematics IX (Proc. 9th Australian Conf. on Combinatorial Mathematics, Univ. of Queensland, Brisbane), Lecture Notes in Mathematics 952, Springer (1982) 89-114.
33. W.L. Kocay, 'Attaching graphs to pseudosimilar vertices', J. Austral. Math. Soc. Ser. A 36 (1984), 53-58.
34. W.L. Kocay, 'Graphs, groups and pseudo-similar vertices', J. Austral. Math. Soc. Ser. A 37 (1984), 181-189.
35. W.L. Kocay, 'On Stockmeyer's non-reconstructible tournaments', J. Graph Theory 9 (1985), 473-476.
36. W.L. Kocay, P. Niesink and C.R. Zarnke, 'On coset diagrams for pseudo-similar vertices', preprint, 1992.
37. I. Krasikov, On the Number Deck of a Tree, Doctoral Thesis, Tel-Aviv University, 1988.
38. I. Krasikov, 'Interchanging branches and similarity in a tree', Graphs and Combinatorics 7 (1991), 165-175.
39. V. Krishnamoorthy, 'Almost-similar vertices in graphs', Combinatorics and Applications, Indian Statist. Inst., Calcutta (1984), 201-209.
40. V. Krishnamoorthy and K.R. Parthasarathy, 'Cospectral graphs and digraphs with given automorphism group', J. Combin. Theory Ser. B 19 (1975), 204-213.
41. V. Krishnamoorthy and K.R. Parthasarathy, 'Similarity concepts in graphs', Rev. Roum. Math. Pures et Appl. (1977), 1253-1258.
42. J. Lauri and M.C. Marino, 'On pseudosimilarity in graphs'. Combinatorics '88 (Proceedings of the International Conference on Incidence Geometries and Combinatorial Structures, Ravello, Italy, 1988, ed. A. Barlotti et al.) Vol. 2 (1991), 169-179.
43. J. Lauri, 'Endvertex-deleted subgraphs', Ars Combinatoria (1992), 36 (1993), 171-182.
44. L. Lovász, Combinatorial Problems and Exercises, North Holland, Amsterdam 1979.
45. B.D. McKay, 'Computer reconstruction of small graphs', J. Graph Theory 1 (1977), 281-283.
46. W.J. Myrvold, 'The ally reconstruction number of a tree with five or more vertices is three', J. Graph Theory 14 (1990), 149-166.
47. G. Prins, The automorphism group of a tree, Doctoral Thesis, University of Michigan, 1957.
48. V. Sankaran and V. Krishnamoorthy, 'Trees with prescribed properties', in Optimization, Design of Experiments and Graph Theory, Indian Inst. Tech., Bombay (1988), 353-355.
49. A.J. Schwenk, 'Removal-cospectral sets of vertices in a graph', Congressus Numerantium 24 (1979), 849-860.
50. P.K. Stockmeyer, 'The falsity of the reconstruction conjecture for tournaments', J. Graph Theory 1 (1977), 19-25.
51. P.K. Stockmeyer, 'A census of non-reconstructible digraphs, I: Six related families', J. Combin. Theory Ser. B 31 (1981), 232-239.
52. P.K. Stockmeyer, 'Tilting at windmills, or my quest for nonreconstructible graphs', Congressus Numerantium 63 (1988), 188-200.
53. R. Taylor, 'Similarity reconstruction of trees', J. Combin. Theory Ser. B 41 (1986), 235-245.
54. C. Thomassen, 'A characterisation of locally finite vertex-transitive graphs', J. Combin. Theory Ser. B 43 (1987), 116-119.
55. P.D. Vestergaard, 'Graphs whose one-edge deletions partition into two isomorphism classes'. Colloquia Mathematica Societatis Janos Bolyai 52. Combinatorics Eger (Hungary) 1987, (ed. A. Hajnal, L. Lovász, V.T. Sós) North-Holland (1988) 527-540.