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On 7-valent symmetric Cayley graphs of finite simple groups

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Abstract

Quite a lot of attention has been paid recently to the classification of symmetric Cayley graphs of non-abelian simple groups. Besides the known complete classification on the cubic case, in most cases, the classifications are conditional with restrictions, such as on specified non-abelian simple groups or on solvable vertex-stabilizers. In this paper, a characterization of the 7-valent symmetric Cayley graphs of finite simple groups is given.

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Acknowledgements

The authors are grateful to the anonymous referees for suggesting a number of improvements and the National Natural Science Foundation of China (11861012), and the first author is grateful for partial support by the NSF of Guangxi (2021GXNSFAA220116), the special foundation for Guangxi Ba Gui Scholars, and the second author is grateful for partial support by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202101304) and NSF of Chongqing (cstc2021jcyj-msxmX0831). The authors also acknowledge the use of the Magma and Gap computational package, which helped show some of the results given in this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, People’s Republic of China

    Jing Jian Li

  2. Chongqing Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, 402160, People’s Republic of China

    Jicheng Ma

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Wenying Zhu

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  1. Jing Jian Li
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  2. Jicheng Ma
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  3. Wenying Zhu
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Correspondence to Jicheng Ma.

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Li, J.J., Ma, J. & Zhu, W. On 7-valent symmetric Cayley graphs of finite simple groups. J Algebr Comb 56, 1097–1118 (2022). https://doi.org/10.1007/s10801-022-01147-w

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  • DOI: https://doi.org/10.1007/s10801-022-01147-w

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