International Journal of Nonlinear Analysis and Applications

Maximal ideal graph of commutative semirings

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Education for Pure Sciences, Thi-Qar University,Thi-Qar, Iraq

Abstract

In this paper, a new kind of graph on a commutative semiring is introduced and investigated. The maximal ideal graph of S, denoted by MG(S), is a graph with all nontrivial ideals of S as vertices and two distinct vertices I and J are adjacent if and only if I + J is a maximal ideal of S. In this article, some interrelation between the graph-theoretic properties of this graph and some algebraic properties of semirings are studied. We investigated the basic properties of the maximal ideal graph such as diameter, girth, clique number, cut vertex, and planar property. 

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 913-926
  • Receive Date: 10 January 2021
  • Revise Date: 02 March 2021
  • Accept Date: 07 March 2021