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arXiv · 2002.02663

Arc-transitive Cayley graphs on nonabelian simple groups with prime valency

Fu-Gang Yin·Yan-Quan Feng·Jin-Xin Zhou·Shan-Shan Chen
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Abstract

In 2011, Fang et al. in (J. Combin. Theory A 118 (2011) 1039-1051) posed the following problem: Classify non-normal locally primitive Cayley graphs of finite simple groups of valency $d$, where either $d\leq 20$ or $d$ is a prime number. The only case for which the complete solution of this problem is known is of $d=3$. Except this, a lot of efforts have been made to attack this problem by considering the following problem: Characterize finite nonabelian simple groups which admit non-normal locally primitive Cayley graphs of certain valency $d\geq4$. Even for this problem, it was only solved for the cases when either $d\leq 5$ or $d=7$ and the vertex stabilizer is solvable. In this paper, we make crucial progress towards the above problems by completely solving the second problem for the case when $d\geq 11$ is a prime and the vertex stabilizer is solvable.

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Fu-Gang Yin, Yan-Quan Feng, Jin-Xin Zhou, Shan-Shan Chen. 2020-02-07. Arc-transitive Cayley graphs on nonabelian simple groups with prime valency. https://arxiv.org/abs/2002.02663

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