Planarity of permutability intersection graph of subgroups of finite groups

Esakkiraj A; P. Devi

doi:10.5269/bspm.81724

Planarity of permutability intersection graph of subgroups of finite groups

Authors

Esakkiraj A Research Scholar, Department of Mathematics, Sri Paramakalyani College, Alwarkurichi- 627 412, Affiliated to Manonmaniam Sundaranar University, Tirunelveli - 627 012, Tamilnadu, India.
P. Devi

DOI:

https://doi.org/10.5269/bspm.81724

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 âˆ© 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.