Asian-European Journal of Mathematics, Volume (14), No (7), Year (2020-9)

Title : ( A graph associated to centralizer of elements of a group )

Authors: Farangis Johari , Kazem Khashyarmanesh ,

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For a given nonabelian finite group G and S ⊆ G\\\\\\\\\\\\\\\\Z(G), where Z(G) denotes the center of G, we introduce a new graph Γ(G, S) associated to the group G as follows: Take G\\\\\\\\\\\\\\\\(S ∪ Z(G)) as its vertex set and two distinct vertices x and y being adjacent if and only if there exists an element s ∈ S such that [x, s] = 1 = [y, s]. This paper is devoted to investigate the properties of graphs Γ(G, S) and establish some graph theoretical properties. Moreover, we describe the planarity of these graphs when |S| = 1. Also, we provide some examples of finite nonabelian groups G with the property that if Γ(G, S)=Γ(H, S) and |S| = 1 for some group H and S\\\\\\\\\\\\\\\' ⊆ H\\\\\\\\\\\\\\\\Z(H), then |G| = |H|.


, Commuting graph; commutator; centralizer; extra, special p, group
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author = {Johari, Farangis and Khashyarmanesh, Kazem},
title = {A graph associated to centralizer of elements of a group},
journal = {Asian-European Journal of Mathematics},
year = {2020},
volume = {14},
number = {7},
month = {September},
issn = {1793-5571},
keywords = {Commuting graph; commutator; centralizer; extra-special p-group},


%0 Journal Article
%T A graph associated to centralizer of elements of a group
%A Johari, Farangis
%A Khashyarmanesh, Kazem
%J Asian-European Journal of Mathematics
%@ 1793-5571
%D 2020