A New Graph Structure of Commutative Semigroups

摘要

In this paper, a new zero-divisor graph overline{G}(S) is defined and studied for a commutative semigroup S with zero element. The properties and the structure of the graph are studied; for any complete graph and complete bipartite graph G, commutative semigroups S are constructed such that the graph G is isomorphic to overline{G}(S).