Elsevier

Discrete Mathematics

Volume 305, Issues 1–3, 6 December 2005, Pages 354-360
Discrete Mathematics

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Automorphism groups of tetravalent Cayley graphs on regular p-groups

https://doi.org/10.1016/j.disc.2005.10.009Get rights and content
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Abstract

Let Cay(G,S) be a connected tetravalent Cayley graph on a regular p-group G and let Aut(G) be the automorphism group of G. In this paper, it is proved that, for each prime p2,5, the automorphism group of the Cayley graph Cay(G,S) is the semidirect product R(G)Aut(G,S) where R(G) is the right regular representation of G and Aut(G,S)={αAut(G)|Sα=S}. The proof depends on the classification of finite simple groups. This implies that if p2,5 then the Cayley graph Cay(G,S) is normal, namely, the automorphism group of Cay(G,S) contains R(G) as a normal subgroup.

Keywords

Cayley graph
Normal Cayley graph
Regular p-group

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Supported by NSFC (10571013) in China.