Author(s)

Li Chen¹, Tongsuo Wu²

¹School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China.
²Department of Mathematics, Shanghai Jiaotong University, Shanghai, China.

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.

Zero-Divisor Semigroup, Sub-Semigroup, Zero-Divisor Graph

Chen, L. and Wu, T. (2023) On a Class of Semigroup Graphs. Advances in Pure Mathematics, 13, 303-315. doi: 10.4236/apm.2023.136021.