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On a Class of Semigroup Graphs
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
Department of Mathematics, Shanghai Jiaotong University, Shanghai, China
- 1 School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
- 2 Department of Mathematics, Shanghai Jiaotong University, Shanghai, China
Advances in Pure Mathematics·Volume 13 (2023)·Pages 303–315·Published 25 June 2023·DOI10.4236/apm.2023.136021
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Abstract
Let G = Γ( S ) be a semigroup graph, i.e. , a zero-divisor graph of a semigroup S with zero element 0. For any adjacent vertices x, y in G , denote C ( x , y ) = { z ∈ V(G) | N ( z ) = { x , y }} . Assume that in G there exist two adjacent vertices x, y , a vertex s ∈ C ( x , y ) and a vertex z such that d ( s , z ) = 3 . This paper studies algebraic properties of S with such graphs G = Γ( S ), giving some sub-semigroups and ideals of S . It constructs some classes of such semigroup graphs and classifies all semigroup graphs with the property in two cases.
KeywordsZero-Divisor SemigroupSub-SemigroupZero-Divisor Graph
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