J Austral Math Soc Ser A 56 pp53--63, 1994.

Vertex-Transitive Graphs which are not Cayley Graphs, I

Brendan D. McKay and Cheryl E. Praeger

(Received 4 July 1990; revised 10 June 1991)

Abstract

The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph which is not a Cayley graph. We consider the problem of determining the orders of such graphs. In this, the first of a series of papers, we present a sequence of constructions which solve the problem for many orders. In particular, such graphs exist for all orders divisible by a fourth power, and all even orders which are divisible by a square.

1991 AMS Subject Classification: primary 05C25; secondary 20B25

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Authors

Brendan D. McKay: Computer Science Department, Australian National University, ACT 0200, Australia.
mailto:bdm@cs.anu.edu.au
Cheryl E. Praeger: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
mailto:praeger@maths.uwa.edu.au

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Last Modified: Fri Jan 10 8:53:40 2003