Some properties of the maximal graph related to co-ideal of a commutative semiring

Yahya Talebi\(^1\)
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.; (Y.T)

Atefeh Darzi

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.; (A.D)

\(^{1}\)Corresponding Author: talebi@umz.ac.ir

Copyright © 2020 Yahya Talebi, Atefeh Darzi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Submitted: 1 December 2017; Accepted: 9 December 2020; Published: 13 March 2020.

Abstract

For a commutative semiring \(R\) with non-zero identity, the maximal graph of \(R\), denoted by \(MG(R)\), is the graph whose vertices are all elements of \(UM(R)\) with two distinct vertices joined by an edge when there is a maximal co-ideal that contains both of them. In this paper, we study some properties of maximal graph such as planarity, radius, splitting and domination number.

Keywords:

Commutative semirings, maximal co-ideal, maximal graph.