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Vertex-transitive graphs which are not Cayley graphs, I

Part of: Graph theory Permutation groups

Published online by Cambridge University Press:  09 April 2009

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

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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.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 1 , February 1994 , pp. 53 - 63
Copyright
Copyright © Australian Mathematical Society 1994

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