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On normal 2-geodesic transitive Cayley graphs

Authors
  • Devillers, Alice1
  • Jin, Wei1, 2
  • Li, Cai Heng1
  • Praeger, Cheryl E.1
  • 1 The University of Western Australia, School of Mathematics and Statistics, Crawley, WA, 6009, Australia , Crawley (Australia)
  • 2 Jiangxi University of Finance and Economics, School of Statistics, Nanchang, Jiangxi, 330013, P.R. China , Nanchang (China)
Type
Published Article
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Publication Date
Sep 11, 2013
Volume
39
Issue
4
Pages
903–918
Identifiers
DOI: 10.1007/s10801-013-0472-7
Source
Springer Nature
Keywords
License
Yellow

Abstract

We investigate connected normal 2-geodesic transitive Cayley graphs Cay(T,S). We first prove that if Cay(T,S) is neither cyclic nor K4[2], then 〈a〉∖{1}⊆̷S for all a∈S. Next, as an application, we give a reduction theorem proving that each graph in this family which is neither a complete multipartite graph nor a bipartite 2-arc transitive graph, has a normal quotient that is either a complete graph or a Cayley graph in the family for a characteristically simple group. Finally we classify complete multipartite graphs in the family.

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