TITLE:
On a Class of Semigroup Graphs
AUTHORS:
Li Chen, Tongsuo Wu
KEYWORDS:
Zero-Divisor Semigroup, Sub-Semigroup, Zero-Divisor Graph
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.6,
June
25,
2023
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, yin G, denote C(x,y) = {z∈V(G) | N (z) = {x,y}}. Assume that in G there exist two adjacent vertices x, y, a vertexs∈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.