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

  • BO LING (a1) and BEN GONG LOU (a2)
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 $\text{A}_{40}$ .

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bengong188@163.com
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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