Annihilator graphs of a commutative semigroup whose Zero-divisor graphs are a complete graph with an end vertex

Abstract

Abstract Suppose that the zero-divisor graph of a commutative semi-group S, be a complete graph with an end vertex. In this paper, we determine the structure of the annihilator graph S and we show that if Z(S)= S, then the annihilator graph S is a disconnected graph.