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Permutation Groups, Vertex-transitive Digraphs and Semiregular Automorphisms

✍ Scribed by D. Maru s̆c̆; R. Scapellato

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
120 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis

A nonidentity element of a permutation group is said to be semiregular if all of its orbits have the same length. The work in this paper is linked to [6] where the problem of existence of semiregular automorphisms in vertex-transitive digraphs was posed. It was observed there that every vertextransitive digraph of order p k or mp, where p is a prime, k ≥ 1 and m ≤ p are positive integers, has a semiregular automorphism. On the other hand, there are transitive permutation groups without semiregular elements [4]. In this paper, it is proved that every cubic vertex-transitive graph contains a semiregular automorphism, and moreover, it is shown that every vertex-transitive digraph of order 2 p 2 , where p is a prime, contains a semiregular automorphism.

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