Title : ( ON THE ANNIHILATOR GRAPH OF GROUP RINGS )
Authors: M. Afkhami , Kazem Khashyarmanesh , sepide salehifar ,
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Abstract
Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for a ∈ Z(R), let ann(a) = {r ∈ R | ra = 0}. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if ann(xy) not eq. ann(x) ∪ ann(y). In this paper, we study the annihilator graph associated to a group ring RG.
Keywords
, zero-divisor graph, annihilator graph, bipartite graph, planar graph, line graph.
@article{paperid:1067045,
author = {M. Afkhami and Khashyarmanesh, Kazem and Salehifar, Sepide},
title = {ON THE ANNIHILATOR GRAPH OF GROUP RINGS},
journal = {Bulletin of the Korean Mathematical Society },
year = {2017},
volume = {54},
number = {1},
month = {July},
issn = {1015-8634},
pages = {331--342},
numpages = {11},
keywords = {zero-divisor graph; annihilator graph; bipartite graph; planar
graph; line graph.},
}
%0 Journal Article
%T ON THE ANNIHILATOR GRAPH OF GROUP RINGS
%A M. Afkhami
%A Khashyarmanesh, Kazem
%A Salehifar, Sepide
%J Bulletin of the Korean Mathematical Society
%@ 1015-8634
%D 2017
