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On Two-Sided Cayley Graphs of Semigroups and Groups

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Abstract

In this paper, first we introduce the notion of two-sided Cayley graph of a semigroup. Then, we investigate some fundamental properties of these graphs and we use our results to give partial answers to some problems raised by Iradmusa and Praeger about two-sided group graphs (two-sided Cayley graphs of groups). Specially, as a consequence of our results, we determine all undirected two-sided Cayley graphs of groups which are connected. Furthermore, by introducing the notion of color-preserving automorphisms of a two-sided Cayley graph of a semigroup (group) and calculating them under some assumptions, we determine the family of color-vertex transitive two-sided Cayley graphs of semigroups (groups).

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Notes

  1. The authors are grateful to the anonymous reviewers for suggesting this problem.

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Acknowledgements

The authors express their gratitude to the referees for very valuable suggestions, which help them to improve the manuscript essentially.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    Farshad Hassani Hajivand & Behnam Khosravi

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  1. Farshad Hassani Hajivand
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  2. Behnam Khosravi
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Correspondence to Behnam Khosravi.

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Communicated by Kolja Knauer.

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Hassani Hajivand, F., Khosravi, B. On Two-Sided Cayley Graphs of Semigroups and Groups. Ann. Comb. 27, 413–432 (2023). https://doi.org/10.1007/s00026-022-00618-y

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