Zero-Divisor Semigroups and Some Simple Graphs

Abstract

In this article, we study commutative zero-divisor semigroups determined by graphs. We prove that for all n ≥ 4, the complete graph K n together with two end vertices has a unique corresponding zero-divisor semigroup, while the complete graph K n together with three end vertices has no corresponding semigroups. We determine all the twenty zero-divisor semigroups whose zero-divisor graphs are the complete graph K 3 together with an end vertex.