arXiv subjects

Liu Weijun

Publications and source records attributed to Liu Weijun.

3 recordsLinked to original sources

arXiv2024

Generalized Cayley graphs of complete groups

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.

math.CO↗

arXiv2024

Generalized Cayley graphs and perfect code

Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.

math.CO↗

arXiv2023

Some properties of generalized Cayley graphs

In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs on abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs on finite groups to be connected. At last, as a by-product, we determine the groups whose all cubic generalized Cayley graphs are connected and integral.

math.CO↗