On realizing zero-divisor graphs of po-semirings

Abstract

In this paper, we determine bipartite graphs and complete graphs with horns, which are realizable as zero-divisor graphs of po-semirings. As applications, we classify commutative rings $R$ whose annihilating-ideal graph $\mathbb {AG}(R)$ are either bipartite graphs or complete graphs with horns.

16 pages, 5 figure