Planarity of permutability intersection graph of subgroups of finite groups
Abstract
Let G be a group. Then the permutability intersection graph of G is a graph and it is denoted
by PI(G) whose vertex set is all the proper subgroups of G and two vertices H, K are adjacent if and only if
they permutes and H ∩ K not equal to {e} . In this paper, we classified all finite groups whose permutability intersection
graph is one of planar, bipartite, C3-free. Also, we have studied some other properties for the same.
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