On a Class of Semigroup Graphs  

作　　者：Li Chen Tongsuo Wu Li Chen;Tongsuo Wu(School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China;Department of Mathematics, Shanghai Jiaotong University, Shanghai, China)

机构地区：[1]School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China [2]Department of Mathematics, Shanghai Jiaotong University, Shanghai, China

出　　处：《Advances in Pure Mathematics》2023年第6期303-315,共13页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Zero-Divisor Semigroup Sub-Semigroup Zero-Divisor Graph 

分 类 号：O15[理学—数学]