arXiv subjects

Qianfen Liao

Publications and source records attributed to Qianfen Liao.

3 recordsLinked to original sources

arXiv2025

Classification of flag-transitive $2$-$(v, k, λ)$ designs with alternating group $A_n$($n \le 10$) as socle

This paper is devoted to the classification of all flag-transitive point-primitive non-trivial $2$-$(v, k, λ)$ designs with the alternating group $A_n$($n \le 10$) as the socle of their automorphism groups, and 87 different designs are obtained up to isomorphism. The results of this study further improve the classification theory of designs under the action of almost simple groups, and provide reference for the follow-up study of similar problems.

math.CO↗

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↗

arXiv2023

The group vertex magicness of unicyclic and bicyclic graphs

In this paper, we give a characterization of unicyclic graphs with diameter at most 4 which are A-vertex magic. Moreover, let G be a bicyclic graph of diameter 3, then G is group vertex magic if and only if G = M11(0, 0).

math.CO↗