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Ideal Graphs Supported By Given Ideals of Commutative Rings

F. H. Abdulqadr1

1Mathematics 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  

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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 JI of R with IJP, and every two vertices I and J are adjacent if IJ 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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