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

Published online by Cambridge University Press:  11 January 2016

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
Corresponding

Abstract

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 $\text{A}_{40}$.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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