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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(S_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> be completely 0-simple semigroups. We provide a necessary and sufficient condition for the power digraph of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(S_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> to be isomorphic to a Cayley graph of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(S_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>. Moreover, we characterize a completely 0-simple semigroup whose power digraph can be represented as a Cayley graph of some completely 0-simple semigroup and describe a completely 0-simple semigroup some of whose Cayley graphs are isomorphic to the power digraph of some completely 0-simple semigroup.</p>

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Cayley graphs and power digraphs over completely 0-simple semigroups

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • Boxing Yang,
  • Yong Shao,
  • Yanliang Cheng,
  • Nuo Wang

摘要

Let \(S_1\) S 1 and \(S_2\) S 2 be completely 0-simple semigroups. We provide a necessary and sufficient condition for the power digraph of \(S_1\) S 1 to be isomorphic to a Cayley graph of \(S_2\) S 2 . Moreover, we characterize a completely 0-simple semigroup whose power digraph can be represented as a Cayley graph of some completely 0-simple semigroup and describe a completely 0-simple semigroup some of whose Cayley graphs are isomorphic to the power digraph of some completely 0-simple semigroup.