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A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF $\text{A}_{39}$

Part of: Representation theory of groups Graph theory Permutation groups

Published online by Cambridge University Press:  11 January 2016

BO LING  and
BEN GONG LOU
BO LING
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunmin 650031, PR China email bolinggxu@163.com
BEN GONG LOU*
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunmin 650031, PR China email bengong188@163.com
*
✉bengong188@163.com
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Abstract

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Zhou and Feng [‘On symmetric graphs of valency five’, Discrete Math. 310 (2010), 1725–1732] proved that all connected pentavalent 1-transitive Cayley graphs of finite nonabelian simple groups are normal. We construct an example of a nonnormal 2-arc transitive pentavalent symmetric Cayley graph on the alternating group $\text{A}_{39}$. Furthermore, we show that the full automorphism group of this graph is isomorphic to the alternating group $\text{A}_{40}$.

Keywords

normal Cayley graphsymmetric graphautomorphism groupfinite simple group

MSC classification

Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20D06: Simple groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 441 - 446
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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