normal subgroup graph of a group

Given any normal subgroup n of a group g, we let γn(g) be the graph with vertex setfx 2 g n n j xy 2 n for some y 2 g n ng, where distinct vertices x and y are adjacent if and only if xy 2 n. in this article, we show that, γn(g)is connected with diam(γn(g)) ≤ 3. furthermore, if γn(g) contains a cycle, then gr(γn(g)) ≤ 7. also,we show that, if n is a nonzero proper normal subgroup of a group g, then γn(g) has no cut-points.