Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T20:44:26.314Z Has data issue: false hasContentIssue false
  • English
  • Français

Vertex-primitive half-transitive graphs

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

D. E. Taylor  and
Ming-Yao Xu
D. E. Taylor
Affiliation:
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
Ming-Yao Xu
Affiliation:
Institute of Mathematics, Peking University, Beijing 100871, People's, Republic of China
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.

Given an infinite family of finite primitive groups, conditions are found which ensure that almost all the orbitals are not self-paired. If p is a prime number congruent to ±1(mod 10), these conditions apply to the groups P S L (2, p) acting on the cosets of a subgroup isomorphic to A5. In this way, infinitely many vertex-primitive ½-transitive graphs which are not metacirculants are obtained.

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures 20B15: Primitive groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 113 - 124
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Alspach, B., Marušiˇ, D. and Nowitz, L., ‘½-arc-transitive grpahs’, preprint, 1991.Google Scholar
[2]Alspach, B. and Parsons, T. D., ‘A construction for vertex-transitive graphs’, Canad. J. Math. 34 (1982), 307–318.CrossRefGoogle Scholar
[3]Alspach, B. and Xu, M.-Y., ‘½-transitive grpahs of order 3p’, preprint, 1991.Google Scholar
[4]Biggs, N., Finite groups of automorphisms, London Mathematical Society Lecture Note Series 6 (Cambridge University Press, 1971).Google Scholar
[5]Bouwer, I. Z., ‘Vertex and edge-transitive but not 1-transitive graphs’, Canad. Math. Bull. 13 (1970), 231–237.CrossRefGoogle Scholar
[6]Dickson, L. E., Linear groups with an exposition of the Galois field theory (Leipzig, 1901; Dover Publ., 1958).Google Scholar
[7]Holt, D. F., ‘A grpah which is edge transitive but not arc-transitive’, Graph Theory 5 (1981), 201–204.CrossRefGoogle Scholar
[8]Holton, D., ‘Research problem 9’, Discrete Math. 38 (1982), 125–126.Google Scholar
[9]Huppert, B., Endliche Gruppen I (Springer-Verlag, 1967).CrossRefGoogle Scholar
[10]Liebeck, M. W., Praeger, C. E., and Saxl, J., ‘A classification of the maximal subgroups of the finite alternating and symmetric groups’, J. Algebra 111 (1987), 365–383.CrossRefGoogle Scholar
[11]Praeger, C. E. and Xu, M.-Y., ‘Vertex primitive grpahs of order a product of two distinct primes’, J. Combin. Theory Ser. B 59 (1993), 245–266.CrossRefGoogle Scholar