Discrete Mathematics, Algorithms and Applications, Volume (7), No (1), Year (2014-2) , Pages (145006801-145006811)

Title : ( A generalization of commuting graphs )

Authors: Mojgan Afkhami , Zahra Barati , Seyede Nesa Hoseini , Kazem Khashyarmanesh ,

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Let R be a ring with the identity element 1, α be an endomorphism of R and b be a left α-derivation. In this paper, we introduce a generalization of a commuting graph, which is denoted by ΓR(α, b), as a directed graph with vertex set R and, for two distinct vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the graph ΓR(α, 0).


Commuting graph; derivation; planar graph; genus.
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author = {Mojgan Afkhami and Zahra Barati and Hoseini, Seyede Nesa and Khashyarmanesh, Kazem},
title = {A generalization of commuting graphs},
journal = {Discrete Mathematics, Algorithms and Applications},
year = {2014},
volume = {7},
number = {1},
month = {February},
issn = {1793-8309},
pages = {145006801--145006811},
numpages = {10},
keywords = {Commuting graph; derivation; planar graph; genus.},


%0 Journal Article
%T A generalization of commuting graphs
%A Mojgan Afkhami
%A Zahra Barati
%A Hoseini, Seyede Nesa
%A Khashyarmanesh, Kazem
%J Discrete Mathematics, Algorithms and Applications
%@ 1793-8309
%D 2014