Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T15:22:02.901Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructions for arc-transitive digraphs

Part of: Graph theory Permutation groups

Published online by Cambridge University Press:  09 April 2009

Marston Conder ,
Peter Lorimer  and
Cheryl Praeger
Marston Conder
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Peter Lorimer
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Cheryl Praeger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands WA 6009, Australia
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.

A number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 61 - 80
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Cameron, P. J., Structure of sub-orbits in some primitive permutation groups (D. Phil. thesis, University of Oxford, 1971).Google Scholar
[2]Cameron, P. J., Praeger, C. E. and Wormald, N. C., ‘Infinite highly arc transitive digraphs and universal covering digraphs,’ Combinatorica 13 (1993), 377–394.Google Scholar
[3]Cannon, J. J., ‘An introduction to the group theory language CAYLEY’, in: Computational group theory (ed. Atkinson, M.) (Academic Press, San Diego CA/London, 1984) pp. 145–183.Google Scholar
[4]Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups, 4th edition (Springer, Berlin, 1980).Google Scholar
[5]Praeger, C. E., ‘Highly arc transitive digraphs’, European J. Combin. 10 (1989), 281–292.Google Scholar
[6]Praeger, C. E., ‘On homomorphic images of edge transitive directed graphs’, Austral. J. Combin. 3 (1991), 207–210.Google Scholar
[7]Weiss, R., ‘The non-existence of 8-transitive graphs’, Combinatorica 1 (1981), 309–311.CrossRefGoogle Scholar
[8]Wielandt, H., Finite permutation groups (Academic Press, New York, 1964).Google Scholar