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arXiv · 2405.00297

Generalized Cayley graphs of complete groups

Qianfen Liao·Liu Weijun
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Abstract

A group $G$ is complete group if it satisfies $Z(G)=e$ and $Aut(G)=Inn(G)$. In this paper, on the one hand, we study the basic properties of generalized Cayley graphs and characterize two classes isomorphic generalized generalized Cayley graphs of complete groups. On the other hand, we give the sufficient and necessary conditions of complete group to be $GCI$ group and restricted $GCI$ group. As an application, we complete the classification of restricted $GCI$-groups for symmetric groups.

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Qianfen Liao, Liu Weijun. 2024-05-06. Generalized Cayley graphs of complete groups. https://arxiv.org/abs/2405.00297

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