Some Results of the Normal Intersection Graph of a Group - Iranmanesh, Ali; Aboomahigir, Elham (Communications in Mathematics and Applications, 2018)
Let \(G\) be a group. We denote the normal intersection graph of subgroups of \(G\) by \(Δ(G)\), and define it as an undirected graph with no loops and multiple edges, whose vertex set is the set of all non-trivial subgroups of \(G\) and two distinct vertices \(H\) and \(K\) are adjacent if and only if \(H\cap K\) is normal in \(G\). In this paper, we characterize all of groups \(G\) whose the normal intersection graph of \(G\) is planar and we investigate some other properties of this graph.