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doi:10.1016/j.ejc.2006.12.001    
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Copyright © 2007 Elsevier Ltd All rights reserved.

Finite 2-arc-transitive abelian Cayley graphs

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Cai Heng Lia, b, E-mail The Corresponding Author and Jiangmin Pana

aDepartment of Mathematics, Yunnan University, Kunming 650031, PR China

bSchool of Mathematics and Statistics, The University of Western Australia, Crawly, WA 6009, Australia


Received 23 February 2005; 
revised 29 September 2005; 
accepted 5 December 2006. 
Available online 30 December 2006.

Abstract

Let Γ be a finite 2-arc-transitive Cayley graph of an abelian group. It is shown that either Γ is explicitly known, or Γ may be represented as a normal or bi-normal Cayley graph of an abelian or a meta-abelian 2-group. In particular, one of three cases occurs: View the MathML source where n is even but is not a 2-power, Γ has 2-power number of vertices, or Γ is a circulant.

Article Outline

1. Introduction
2. A reduction to a primitive or bi-primitive case
3. Primitive and bi-primitive cases
4. Proof of Theorem 1.1
Acknowledgements
References

 
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