Title : ( The Coannihilator Graph of a Commutative Ring )
Authors: Mojgan Afkhami , Kazem Khashyarmanesh , zohreh rajabi ,
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Abstract
Let R be a commutative ring with nonzero identity. In this paper we intro- duce the coannihilator graph of R, which is a dual of the annihilator graph AG(R), denoted by AG0(R). AG0(R) is a graph with the vertex set W(R), where W(R) is the set of all nonzero and nonunit elements of R, and two distinct vertices x and y are adjacent if and only if x /2 xyR or y /2 xyR, where for z 2 R, zR is the principal ideal generated by z. We study the interplay between the ring-theoretic properties of R and graph-theoretic properties of AG(R).
Keywords
, Coannihilator graph; Annihilator graph; Zero, divisor graph; Planar; Out, erplanar; Ring graph; Cut vertex; Domination number.
@article{paperid:1078817,
author = {Mojgan Afkhami and Khashyarmanesh, Kazem and Rajabi, Zohreh},
title = {The Coannihilator Graph of a Commutative Ring},
journal = {Southeast Asian Bulletin of Mathematics},
year = {2019},
volume = {1},
number = {43},
month = {July},
issn = {0129-2021},
pages = {1--11},
numpages = {10},
keywords = {Coannihilator graph; Annihilator graph; Zero-divisor graph; Planar; Out-
erplanar; Ring graph; Cut vertex; Domination number.},
}
%0 Journal Article
%T The Coannihilator Graph of a Commutative Ring
%A Mojgan Afkhami
%A Khashyarmanesh, Kazem
%A Rajabi, Zohreh
%J Southeast Asian Bulletin of Mathematics
%@ 0129-2021
%D 2019
