#### Title

Sylow subgraphs of self-complementary vertex transitive graphs

#### Document Type

Article

#### Publication Date

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*^{m} 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.

#### ISSN

0723-0869

#### WorldCat Link

#### Citation

Beezer, R.A. "Sylow Subgraphs in Self-Complementary Vertex Transitive Graphs." Expositiones Mathematicae. 24.2 (2006): 185-194. Print.