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# Ideal Graphs Supported By Given Ideals of Commutative RingsF. H. Abdulqadr11Mathematics Department, College of Education, Salahaddin University, Erbil-Iraq

Original: 9  November 2019       Revised: 12 January 2019      Accepted: 30 January 2020         Published online: 20 June 2020

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

Key Words: Ideal graph supported by given ideals of commutative rings, connected graphs , Clique and chromatic number.

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