On realizing zero-divisor graphs of po-semirings

TL;DR

This paper characterizes which bipartite and complete graphs with horns can be represented as zero-divisor graphs of po-semirings and applies these results to classify certain commutative rings based on their annihilating-ideal graphs.

Contribution

It provides a complete characterization of bipartite and complete graphs with horns as zero-divisor graphs of po-semirings and applies these to classify rings by their annihilating-ideal graphs.

Findings

Bipartite graphs realizable as zero-divisor graphs of po-semirings identified.

Complete graphs with horns realizable as zero-divisor graphs of po-semirings identified.

Classification of rings with bipartite or complete annihilating-ideal graphs achieved.

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.