J Austral Math Soc Ser A 59 pp61--80, 1995.

Constructions for Arc-Transitive Digraphs

Marston Conder, Peter Lorimer and Cheryl Praeger

Abstract

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.

1991 AMS Subject Classification: 05C25, 20B25

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Authors

Marston Conder

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand.

Peter Lorimer

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand.

Cheryl Praeger

Department of Mathematics, University of Western Australia, Nedlands WA 6009, Australia.