Title

Sylow Subgraphs In Self-complementary Vertex Transitive Graphs

Document Type

Article

Publication Date

1-1-2006

Publication Title

Expositiones Mathematicae

Department

Mathematics and Computer Science

Abstract

A graph is self-complementary if it is isomorphic to its complement. A graph is vertex transitive if for each choice of vertices u and v there is an automorphism that carries the vertex u to v. The number of vertices in a self-complementary vertex-transitive graph must necessarily be congruent to 1 mod 4. However, Muzychuk has shown that if p is the largest power of a prime p dividing the order of a self-complementary vertex-transitive graph, then p(m) must individually be congruent to 1 mod 4. This is accomplished by establishing the existence of a self-complementary vertex transitive subgraph of order p(m), a result reminiscent of the Sylow theorems. This article is a self-contained survey, culminating with a detailed proof of Muzychuk's result.

Volume

24

Issue

2

pp.

185-194

ISSN

1089-5639