Intersection graphs of co-ideals of semirings

Abstract

Let R be a semiring with identity. In this paper, we introduce the intersection graph of co-ideals, denoted by G(R). The vertices of G(R) are non-trivial co-ideals of R, and two distinct vertices I and J are adjacent if and only if I∩J≠{1}. The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of R and the graph-theoretic structure of G(R) is investigated.