Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T04:29:53.823Z Has data issue: false hasContentIssue false
  • English
  • Français

ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  13 August 2015

JING CHEN ,
CAI HENG LI  and
WEI JUN LIU
JING CHEN*
Affiliation:
Department of Mathematics, Hunan First Normal University, Changsha 410205, PR China Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou 350003, PR China email [email protected]
CAI HENG LI
Affiliation:
Center for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley 6009 WA, Australia email [email protected]
WEI JUN LIU
Affiliation:
School of Mathematics, Central South University, Changsha 410075, PR China email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the isomorphism problem of vertex-transitive cubic graphs which have a transitive simple group of automorphisms.

Keywords

coset graphisomorphismsGI-graphsvertex-transitive

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 3 , December 2015 , pp. 341 - 349
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Ádám, A., ‘Research problem 2–10’, J. Combin. Theory 2 (1967), 393.Google Scholar
Alspach, B., ‘Isomorphisms of Cayley graphs on abelian groups’, NATO ASI Ser. C 497 (1997), 1–23.Google Scholar
Alspach, B. and Parsons, T. D., ‘Isomorphisms of circulant graphs and digraphs’, Discrete Math. 25 (1979), 97–108.CrossRefGoogle Scholar
Babai, L., ‘Isomorphism problem for a class of point-symmetric structures’, Acta Math. Acad. Sci. Hungar. 29 (1977), 329–336.CrossRefGoogle Scholar
Biggs, N., Algebraic Graph Theory, 2nd edn (Cambridge University Press, New York, 1992).Google Scholar
Dixon, J. D. and Mortimer, B., Permutation Groups (Springer, Berlin, 1996).CrossRefGoogle Scholar
Dobson, E., ‘Isomorphism problem for Cayley graph of Z p3’, Discrete Math. 147 (1995), 87–94.CrossRefGoogle Scholar
Dobson, E., ‘Isomorphism problem for metacirculant graphs of order a product of distinct primes’, Canad. J. Math. 50 (1998), 1176–1188.CrossRefGoogle Scholar
Dobson, E., ‘On the Cayley isomorphism problem for ternary relational structures’, J. Combin. Theory Ser. A 101 (2003), 225–248.CrossRefGoogle Scholar
Fang, X. G., Li, C. H., Wang, J. and Xu, M. Y., ‘On cubic Cayley graph of finite simple groups’, Discrete Math. 224 (2002), 67–75.CrossRefGoogle Scholar
Giudici, M., ‘Factorisations of sporadic simple groups’, J. Algebra 304 (2006), 311–323.CrossRefGoogle Scholar
Godsil, C. D., ‘On the full automorphism group of a graph’, Combinatorica 1 (1981), 243–256.CrossRefGoogle Scholar
Godsil, C. D., ‘On Cayley graph isomorphisms’, Ars Combin. 15 (1983), 231–246.Google Scholar
Godsil, C. and Royle, G., Algebraic Graph Theory (Springer, New York, 2001).CrossRefGoogle Scholar
Guralnick, R. M., ‘Subgroups of prime power index in a simple group’, J. Algebra 81 (1983), 304–311.CrossRefGoogle Scholar
Gross, F., ‘Conjugacy of odd order Hall subgroups’, Bull. Lond. Math. Soc. 19 (1987), 311–319.CrossRefGoogle Scholar
Kleidman, P. and Liebeck, M., The Subgroup Structure of the Finite Classical Groups (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
Kovács, I. and Muzychuk, M., ‘The group Z p2 × Z q is a CI-group’, Comm. Algebra 37 (2009), 3500–3515.CrossRefGoogle Scholar
Li, C. H., ‘On isomorphisms of finite Cayley graphs—a survey’, Discrete Math. 256 (2002), 301–334.CrossRefGoogle Scholar
Muzychuk, M., ‘A solution of the isomorphism problem for circulant graphs’, Proc. Lond. Math. Soc. (3) 88 (2004), 1–41.CrossRefGoogle Scholar
Pálfy, P. P., ‘Isomorphism problem for relational structures with a cyclic automorphism’, European J. Combin. 8 (1987), 35–43.CrossRefGoogle Scholar
Praeger, C. E., ‘An O’Nan–Scott theorem for finite quasiprimitive permutation groups and an application to 2-arc transitive graphs’, J. Lond. Math. Soc. (2) 47 (1993), 227–239.CrossRefGoogle Scholar
Somlai, G., ‘Elementary Abelian p-groups of rank 2p + 3 are not CI-groups’, J. Algebraic Combin. 34 (2011), 323–335.CrossRefGoogle Scholar
Spiga, P., ‘Elementary Abelian p-groups of rank greater than or equal to 4p − 2 are not CI-groups’, J. Algebraic Combin. 26 (2007), 343–355.CrossRefGoogle Scholar
Suzuki, M., Group Theory II (Springer, New York, 1985).Google Scholar
Tutte, W. T., ‘On the symmetry of cubic graphs’, Canad. J. Math. 11 (1959), 621–624.CrossRefGoogle Scholar
Tyshkevich, R. I. and Tan, N. D., ‘A generalisation of Babai’s lemma on Cayley graphs’, Vestsi Nats. Akad. Navuk Belarusi Ser. Fiz.-Mat. Navuk 124 (1987), 29–32.Google Scholar