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Vertex-transitive graphs: Symmetric graphs of prime valency

✍ Scribed by Peter Lorimer

Publisher: John Wiley and Sons
Year: 1984
Tongue: English
Weight: 642 KB
Volume: 8
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190080107

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✦ Synopsis

Let G be a group acting symmetrically on a graph 2, let G, be a subgroup of G minimal among those that act symmetrically on 8, and let G2 be a subgroup of G, maximal among those normal subgroups of GI which contain no member except 1 which fixes a vertex of Z. The most precise result of this paper is that if Z has prime valency p , then either Z is a bipartite graph or G2 acts regularly on Z or GI I G2 is a simple group which acts symmetrically on a graph of valency p which can be constructed from C and does not have more vertices than 2. The results on vertextransitive groups necessary to establish results like this are also included.

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