On a class of semigroup graphs

Li Chen, Tongsuo Wu

Let $G=\Gamma (S)$ 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\in V(G) | N(z)={x,y…