a graph associated with minimal ideals of a ring

In this paper, a new kind of graph is introduced and investigated. the minimal ideal graph for a ring r with unity is an undirected graph whose vertex set contains all non-trivial ideals of r. we denote the graph by mi(r) and the vertex set by v (mi(r)). two vertices p,q ∈ v (mi(r)) are adjacent if aminimal ideal p of r exists with p ⊂ p and p ⊂ q. we study the correlation of algebraic properties and graph theoretic properties of mi(r). in this article, connectedness, diameter, clique number,chromatic number, regular character, cut vertex etc. are discussed.