Abstract
A Cayley graph over a group G is said to be central if its connection set is a normal subset of G. We prove that every central Cayley graph over a simple group G has at most two pairwise nonequivalent Cayley representations over G associated with the subgroups of \({{\,\mathrm{Sym}\,}}(G)\) induced by left and right multiplications of G. We also provide an algorithm which, given a central Cayley graph \(\Gamma \) over an almost simple group G whose socle is of a bounded index, finds the full set of pairwise nonequivalent Cayley representations of \(\Gamma \) over G in time polynomial in size of G.
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The authors are grateful to Prof. Ilia Ponomarenko for fruitful discussions and helpful suggestions.
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J. Guo was supported by the National Natural Science Foundation of China (No. 11961017), W. Guo and A. V. Vasil’ev were supported by the National Natural Science Foundation of China (No. 12171126), and G. Ryabov was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.
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Guo, J., Guo, W., Ryabov, G. et al. On Cayley representations of central Cayley graphs over almost simple groups. J Algebr Comb 57, 227–237 (2023). https://doi.org/10.1007/s10801-022-01166-7
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DOI: https://doi.org/10.1007/s10801-022-01166-7