Title : ( ON THE RELATIVE NON-COMMUTING GRAPH )
Authors: Mehdi Hassankhani , Abbas Jafarzadeh , Abbas Mohammadian ,
Full TextAbstract
Let $G$ be a non-abelian group and $H$ a subgroup of $G$. We associate a graph $\Gamma_{(G,H)}$ to $H$ and $G$ as follows: Take $G_C_G(H)$ as the vertices of $\Gamma_{(G,H)}$ and join two distinct vertices $x$ and $y$, whenever $x$ or $y$ in $H$ and $[x,y]\neq 1$. In this talk we prove that $\Gamma_{(G,H)}$ neither planar nor regular. Moreover, we show that if $\Gamma_{(G_1,H_1)}\cong\Gamma_{(G_2,H_2)}$, then $\Gamma_{H_1}\con\Gamma_{H_2}$.
Keywords
, relative non-commuting graph, planar, regular
@inproceedings{paperid:1067009,
author = {Hassankhani, Mehdi and Jafarzadeh, Abbas and Mohammadian, Abbas},
title = {ON THE RELATIVE NON-COMMUTING GRAPH},
booktitle = {The 7th Algebraic Combinatorics Conference of Iran},
year = {2014},
location = {مشهد, IRAN},
keywords = {relative non-commuting graph; planar; regular},
}
%0 Conference Proceedings
%T ON THE RELATIVE NON-COMMUTING GRAPH
%A Hassankhani, Mehdi
%A Jafarzadeh, Abbas
%A Mohammadian, Abbas
%J The 7th Algebraic Combinatorics Conference of Iran
%D 2014
