A census of semisymmetric cubic graphs on up to 768 vertices

Journal of Algebraic Combinatorics

Volumn 23, Issue 3, 2006, Pages 255-294

  Conder, Marston ^a   Malnič, Aleksander ^b   Marušič, Dragan ^b   Potočnik, Primž ^c  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c UNIVERSITY OF PRIMORSKA   (Slovenia)

Author keywords

Amalgams; Edge transitive graphs; Semisymmetric graphs

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; LINEAR ALGEBRA; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

AUTOMORPHISM; EDGE-TRANSITIVE GRAPHS; SEMISYMMETRIC CUBIC GRAPHS;

GRAPH THEORY;

EID: 33744813293     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-006-7397-3     Document Type: Article

References (40)

1. W. Bosma, C. Cannon, and C. Playoust, "The MAGMA algebra system I: The user language," J. Symbolic Comput. 24 (1997), 235-265.
2. I.Z. Bouwer, "An edge but not vertex transitive cubic graph," Bull Can. Math. Soc. 11 (1968), 533-535.
3. I.Z. Bouwer, "On edge but not vertex transitive regular graphs," J. Combin. Theory, B 12 (1972), 32-40.
4. I.Z. Bouwer (ed.), The Foster Census, Charles Babbage Research Centre, Winnipeg, 1988.
5. M.D.E. Conder and P. Lorimer, "Automorphism Groups of Symmetric Graphs of Valency 3," J. Combin. Theory, Series B 47 (1989), 60-72.
6. M.D.E. Conder, P. Dobcsányi, B. Mc Kay and G. Royle, The Extended Foster Census, http://www.es.uwa.edu.au/~gordon/remote/foster/.
7. M.D.E. Conder and P. Dobcsányi, "Trivalent symmetric graphs on up to 768 vertices," J. Combin. Math. Combin. Comput. 40 (2002), 41-63.
8. M.D.E. Conder, A. Malnič, D. Marušič, T. Pisanski and P. Potočnik, "The edge-transitive but not vertex-transitive cubic graph on 112 vertices", J. Graph Theory 50 (2005), 25-42.
9. J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, and R.A. Wilson, Atlas of finite groups, Oxford University Press, Eynsham, 1985.
10. J.D. Dixon and B. Mortimer, Permutation Groups, Springer-Verlag, New York, 1996.
11. D.Ž. Djoković and G.L. Miller, "Regular groups of automorphisms of cubic graphs," J. Combin. Theory. B 29 (1980), 195-230.
12. P. Dobcsányi, Home Page, http://www.scitec.auckland.ac.nz/~peter.
13. S.F. Du and D. Marušič, "Biprimitive graphs of smallest order," J. Algebraic Combin. 9 (1999), 151-156.
14. S.F. Du and M.Y. Xu, "A classification of semisymmetric graphs of order 2pq (I)," Comm. Algebra 28 (2000), 2685-2715.
15. J. Combin. Theory, Series B 29 (1980), 195-230.
16. J. Folkman, "Regular line-symmetric graphs," J. Combin. Theory 3 (1967), 215-232.
17. R. Frucht, "A canonical representation of trivalent Hamiltonian graphs," J. Graph Theory 1 (1977), 45-60.
18. M. Giudici, C.H. Li and C.E. Praeger, "Characterising finite locally s-arc transitive graphs with a star normal quotient," preprint.
19. C. Godsil, "On the full automorphism group of Cayley graphs," Combinatorica 1 (1981), 143-156.
20. C. Godsil and G. Royle, Algebraic Graph Theory, Graduate Texts in Mathematics 207, Springer-Verlag, New York, 2001.
21. D. Goldschmidt, "Automorphisms of trivalent graphs," Ann. Math. 111 (1980), 377-406.
22. D. Gorenstein, Finite Groups, Harper and Row, New York, 1968.
23. D. Gorenstein, Finite Simple Groups: An Introduction To Their Classification, Plenum Press, New York, 1982.
24. J.L. Gross and T.W. Tucker, Topological Graph Theory, Wiley-Interscience, New York, 1987.
25. M.E. Iofinova and A.A. Ivanov, Biprimitive cubic graphs, Investigations in Algebraic Theory of Combinatorial Objects (Proceedings of the seminar, Institute for System Studies, Moscow, 1985) Kluwer Academic Publishers, London, 1994, pp 459-472.
26. A.V. Ivanov, "On edge but not vertex transitive regular graphs," Ann. Discrete Math. 34 ( 1987), 273-286.
27. M.H. Klin, "On edge but not vertex transitive graphs," Coll. Math. Soc. J. Bolyai, (25. Algebraic Methods in Graph Theory, Szeged, 1978), Budapest, 1981, 399-403.
28. F. Lazebnik and R. Viglione, "An infinite series of regular edge- but not vertex-transitive graphs," J. Graph Theory 41 (2002), 249-258.
29. S. Lipschutz and M.Y. Xu, "Note on infinite families of trivalent semisymmetric graphs," European J. Combin. 23 (2002), 707-711.
30. A. Malnič, D. Marušič and P. Potočnik, "On cubic graphs admitting an edge-transitive solvable group", J. Algebraic Combinatorics 20 (2004), 99-113.
31. A. Malnič, D. Marušič, P. Potočnik and C.Q. Wang, "An infinite family of cubic edge- but not vertex-transitive graphs", Discrete Mathematics 280 (2004), 133-148.
32. A. Malnič, D. Marušič and P. Potočnik, "Elementary abelian covers of graphs", J. Algebraic Combinatorics 20 (2004), 71-97.
33. A. Malnič, R. Nedela, and M. Škoviera, "Lifting graph automorphisms by voltage assignments," European J. Combin. 21 (2000), 927-947.
34. D. Marušič, "Constructing cubic edge- but not vertex-transitive graphs," J. Graph Theory 35 (2000), 152-160.
35. D. Marušič and T. Pisanski, "The Gray graph revisited," J. Graph Theory 35 (2000), 1-7.
36. D. Marušič and P. Potočnik, "Semisymmetry of generalized Folkman graphs," European J. Combin. 22 (2001), 333-349.
37. M. Škoviera, "A contribution to the theory of voltage graphs," Discrete Math. 61 (1986), 281-292.
38. W.T. Tutte, "A family of cubical graphs," Proc. Cambridge Phil. Soc. 43 (1948), 459-474.
39. H. Wielandt, Finite Permutation Groups, Academic Press, New York-London, 1964.
40. S.E. Wilson, "A worthy family of semisymmetric graphs", DiscreteMath. 271 (2003), 283-294.