Let G be a finite group and let N be a fixed normal subgroup of G.In flunazine injection this paper, a new kind of graph on G, namely the intersection graph is defined and studied.We use to denote this graph, with its vertices are all normal subgroups of G and two distinct vertices are adjacent if their intersection in N.
We show some properties of this graph.For instance, the intersection graph is a simple connected with diameter at most two.Furthermore we give the graph structure of for some finite groups such ellakai as the symmetric, dihedral, special linear group, quaternion and cyclic groups.