Relative non-Normal Graphs of a Subgroup of Finite Groups

Author(s):

M. Ziaaddini , A. Erfanian*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or outerplanar.

Keywords:

Non-normal graph , Relative Non-normal graph , Normality degree , Outer planar

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:16 Issue: 1, May 2021
Pages:
181 to 189
https://www.magiran.com/p2262249