Ideal Graphs Supported By Given Ideals of Commutative Rings

Volume 22 , Issue 1 , January 2020 , Pages 217-222

Authors

Fryad H. Abdulqadr 1

1 Mathematics Department, College of Education, Salahaddin University, Erbil-Iraq

DOI logo 10.17656/jzs.10786

Keywords

Abstract

In this paper we introduce and study a new kind of graph that constructed by non-
trivial ideals of a commutative ring with identity. Let R be a commutative ring with

identity and P be a non-trivial ideal of R. The ideal graph supported by the ideal P,
denoted by G(P), is the undirected graph whose vertices are those non-trivial
ideals I of R such that there exists a non-trivial ideal JI of R with IJ⊂P, and every
two vertices I and J are adjacent if IJ and IJ⊂P. We investigate the connectivity,
completeness and planarity of the graph G(P). Also we explore the diameter, girth,
domination, clique number and chromatic number of G(P).

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  • Published at30 January 2020

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