On a Class of Semigroup Graphs

Let G = Γ(S) be a semigroup graph, i.e., zero-divisor graph of 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 there exist two y, vertex s∈C(x,y) and z such d (s,z) 3. This paper studies algebraic properties graphs Γ(S), giving some sub-semigroups ideals S. It constructs classes classifies all the property cases.