On symmetric bi-Cayley graphs of prime valency on nonabelian simple groups

Ran Ju¹ ; Jing jian Li² ; Zai ping Lu³

¹Guangxi University
²Guangxi University
³Nankai University

The electronic journal of combinatorics, Tome 31 (2024) no. 1

Résumé

Let $\Gamma$ be a bipartite graph, and let $\mathrm{Aut}\Gamma$ be the full automorphism group of the graph $\Gamma$. A subgroup $G\leqslant \mathrm{Aut}\Gamma$ is said to be bi-regular on $\Gamma$ if $G$ preserves the bipartition and acts regularly on both parts of $\Gamma$, while the graph $\Gamma$ is called a bi-Cayley graph of $G$ in this case. A subgroup $X\leqslant \mathrm{Aut} \Gamma$ is said to be bi-quasiprimitive on $\Gamma$ if the bipartition-preserving subgroup of $X$ is a quasiprimitive group on each part of $\Gamma$. In this paper, a characterization is given for the connected bi-Cayley graphs on nonabelian simple groups which have prime valency and admit bi-quasiprimitive groups.

Détail

DOI : 10.37236/12085

Classification : 05C25, 20B25
Mots-clés : bi-Cayley graph, prime valency, nonabelian simple group, quasiprimitive group