Ideal Graphs Supported By Given Ideals of Commutative Rings - Abdulqadr, Fryad H. (Sulaimani Journal for Pure and Applied Sciences, 2020)
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).
Keywords: Ideal graph supported by given ideals of commutative rings; connected graphs; Clique and chromatic number