Ideal-based quasi zero divisor graph

WOS:000731750000007Let R be a commutative ring with identity and I a proper ideal of R. In this paper we introduce the ideal-based quasi zero divisor graph Q Gamma(I)(R) of R with respect to I which is an undirected graph with vertex set V = {a is an element of R\root I : ab is an element of I for some b is an element of R\root I} and two distinct vertices a and b are adjacent if and only if ab is an element of I. We study the basic properties of this graph such as diameter, girth, dominaton number, etc. We also investigate the interplay between the ring theoretic properties of a Noetherian multiplication ring R and the graph-theoretic properties of Q Gamma(I)(R)