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Ideal Graphs Supported By Given Ideals of Commutative Rings
Fryad H. Abdulqadr1
1Mathematics Department, College of Education, Salahaddin University, Erbil-Iraq
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
Doi Link; https://doi.org/10.17656/jzs.10786
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 JI of R with IJ⊂P, and every two vertices I and J are adjacent if I
J and IJ⊂P. 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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