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Constructions for arc-transitive digraphs

Part of: Permutation groups Graph theory

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
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Abstract

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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

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