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SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS OF ORDER A PRODUCT OF TWO PRIMES

Part of: Algebraic combinatorics Graph theory

Published online by Cambridge University Press:  13 June 2013

CAI HENG LI  and
GUANG RAO
CAI HENG LI
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia email cai.heng.li@uwa.edu.au
GUANG RAO*
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia email cai.heng.li@uwa.edu.au
*
✉generalrao@hotmail.com
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Abstract

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In this short paper, we characterise graphs of order $pq$ with $p, q$ prime which are self-complementary and vertex-transitive.

Keywords

self-complementaryvertex-transitive

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05E18: Group actions on combinatorial structures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 322 - 330
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Alspach, B., Morris, J. and Vilfred, V., ‘Self-complementary circulant graphs’, Ars Combin. 53 (1999), 187–191.Google Scholar
Beezer, R. A., ‘Sylow subgraphs in self-complementary vertex transitive graphs’, Expo. Math. 24 (2) (2006), 185–194.Google Scholar
Fronček, D., Rosa, A. and Širáň, J., ‘The existence of selfcomplementary circulant graphs’, European J. Combin. 17 (1996), 625–628.Google Scholar
Godsil, C. D., ‘On Cayley graphs isomorphisms’, Ars Combin. 15 (1983), 231–246.Google Scholar
Guralnick, R. M., Li, C. H., Praeger, C. E. and Saxl, J., ‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc. 356 (2004), 4857–4872.Google Scholar
Jajcay, R. and Li, C. H., ‘Constructions of self-complementary circulants with no multiplicative isomorphisms’, European J. Combin. 22 (8) (2001), 1093–1100.Google Scholar
Li, C. H., ‘On self-complementary vertex-transitive graphs’, Comm. Algebra 25 (1997), 3903–3908.Google Scholar
Li, C. H., ‘On finite graphs that are self-complementary and vertex-transitive’, Australas. J. Combin. 18 (1998), 147–155.Google Scholar
Li, C. H. and Praeger, C. E., ‘Self-complementary vertex-transitive graphs need not be Cayley graphs’, Bull. Lond. Math. Soc. 33 (6) (2001), 653–661.Google Scholar
Li, C. H. and Praeger, C. E., ‘On partitioning the orbitals of a transitive permutation group’, Trans. Amer. Math. Soc. 355 (2003), 637–653.Google Scholar
Liskovets, V. and Poschel, R., ‘Non-Cayley-isomorphic self-complementary circulant graphs’, J. Graph Theory 34 (2000), 128–141.3.0.CO;2-I>CrossRefGoogle Scholar
Mathon, R., ‘On selfcomplementary strongly regular graphs’, Disc. Math. 69 (1988), 263–281.Google Scholar
Muzychuk, M., ‘On Sylow subgraphs of vertex-transitive self-complementary graphs’, Bull. Lond. Math. Soc. 31 (5) (1999), 531–533.Google Scholar
Peisert, W., ‘All self-complementary symmetric graphs’, J. Algebra 240 (2001), 209–229.CrossRefGoogle Scholar
Rao, S. B., ‘On regular and strongly regular selfcomplementary graphs’, Disc. Math. 54 (1985), 73–82.Google Scholar
Sachs, H., ‘Über selbstcomplementäre Graphen’, Publ. Math. Debrecen 9 (1962), 270–288.Google Scholar
Suprunenko, D. A., ‘Selfcomplementary graphs’, Cybernetics 21 (1985), 559–567.Google Scholar
Suzuki, M., Group Theory I (Springer, New York, 1986).Google Scholar
Xu, M. Y., ‘Automorphism groups and isomorphisms of Cayley digraphs’, Discrete Math. 182 (1–3) (1998), 309–319.CrossRefGoogle Scholar
Zelinka, B., ‘Self-complementary vertex-transitive undirected graphs’, Math. Slovaca 29 (1979), 91–95.Google Scholar
Zhang, H., ‘Self-complementary symmetric graphs’, J. Graph Theory 16 (1992), 1–5.Google Scholar