Intersection graphs of co-ideals of semirings

Year 2019, Volume: 68 Issue: 1, 840 - 851, 01.02.2019

S. Ebrahimi Atani , Saboura Dolati Pishhesari Mehdi Khoramdel , Zahra Ebrahimi Sarvandi

https://doi.org/10.31801/cfsuasmas.481603

Cited By: 1

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.

Keywords

Co-ideal, intersection graph, I-semiring

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