Title : ( The non-coprime graph of a finite group with respect to a subgroup )
Authors: gholamreza Aghababaei Beni , A. R. ASHRAFI , Abbas Jafarzadeh ,
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Abstract
The non-coprime graph $\Pi_{G,H}$ of a fi nite group G with respect to a subgroup H is a simple graph with $G\ {e}$ as the vertex set. Two vertices u and v of this graph are adjacent if and only if (|u|,|v|) ̸= 1 and u \in H or v \in H. In this paper, the main properties of this graph are obtained. The isomorphism problem of this graph is also investigated for nilpotent groups.
Keywords
, Non-coprime graph, nilpotent group, Mathieu group.
@article{paperid:1067393,
author = {Aghababaei Beni, Gholamreza and A. R. ASHRAFI and Jafarzadeh, Abbas},
title = {The non-coprime graph of a finite group with respect to a subgroup},
journal = {Italian Journal of Pure and Applied Mathematics},
year = {2016},
volume = {38},
month = {June},
issn = {1126-8042},
pages = {1--2},
numpages = {1},
keywords = {Non-coprime graph; nilpotent group; Mathieu group.},
}
%0 Journal Article
%T The non-coprime graph of a finite group with respect to a subgroup
%A Aghababaei Beni, Gholamreza
%A A. R. ASHRAFI
%A Jafarzadeh, Abbas
%J Italian Journal of Pure and Applied Mathematics
%@ 1126-8042
%D 2016
