An explicit characterization of cubic symmetric bi-Cayley graphs on nonabelian simple groups

Pan, Jiangmin; Zhang, Yingnan

doi:10.1016/j.disc.2022.112954

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2024

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“…In the past three decades, bi-Cayley graphs have been involved deeply in many fields of graph theory and played an important role. In particular, many research works have been published about bi-Cayley graphs regarding their strong regularity [9,20,30,31], automorphism [26,40], semisymmetry [27], classification [5,19,32,39], connectivity [3,25], extendability [17,29] and spectrum [16].…”

Section: Introductionmentioning

confidence: 99%

On Symmetric bi-Cayley Graphs of Prime Valency on Nonabelian Simple Groups

Ju,

Li,

2024

Electron. J. Combin.

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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.

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