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Cheng, Yanliang; Shao, Yong; Zeng, Lingli

Power graphs of a class of completely 0-simple semigroups. (English) Zbl 1536.05226

J. Algebr. Comb. 59, No. 3, 697-710 (2024).
Summary: We first determine the structure of the power digraphs of completely 0-simple semigroups, and then some properties of their power graphs are given. As the main result in this paper, using P. J. Cameron and S. Ghosh’s theorem [Discrete Math. 311, No. 13, 1220–1222 (2011; Zbl 1276.05059)] about power graphs of abelian groups, we obtain a characterization that two \(G^0\)-normal completely 0-simple orthodox semigroups \(S\) and \(T\) with abelian group \(\mathcal{H}\)-classes are isomorphic based on their power graphs. We also present an algorithm to determine that \(S\) and \(T\) are isomorphic or not.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures

Keywords:

power graph; completely 0-simple semigroup; Green’s relations; automorphisms of a semigroup

Citations:

Zbl 1276.05059
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Full Text: DOI

References:

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