ON INTERSECTION GRAPH OF A GROUP

. Let G be a group. The intersection graph of G denoted by Γ(G), is the graph whose vertex set is the set of all non-trivial proper subgroups of G and two distinct vertices H and K are adjacent if and only if H \ K ̸ = 1. And we denote the complement of Γ(G) by Λ(G). In this talk we show the diameter of every connected component of Λ(G) does not exceed 3. We characterize all abelian groups whose complememt intersection graphs are conected. Moreover, we show that if Λ(G) is triangle-free, then Λ(G) is bipart graph. In this talk, we classify all finite groups of odd order whose intersection graphs are triangle-free graph.Finally We characterize the domination number of the intersection graph of G whenever G is an abelian group or a finite nilpotent group which is not a