%0 Journal Article %T On a Class of Semigroup Graphs %A Li Chen %A Tongsuo Wu %J Advances in Pure Mathematics %P 303-315 %@ 2160-0384 %D 2023 %I Scientific Research Publishing %R 10.4236/apm.2023.136021 %X Let G = ŚŁ(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) = {zĄĘV(G) | N (z) = {x,y}}. Assume that in G there exist two adjacent vertices x, y, a vertex sĄĘC(x,y) and a vertex z such that d (s,z) = 3. This paper studies algebraic properties of S with such graphs G = ŚŁ(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. %K Zero-Divisor Semigroup %K Sub-Semigroup %K Zero-Divisor Graph %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125768