Southeast Asian Bulletin of Mathematics, Volume (35), No (1), Year (2011-6) , Pages (753-762)

Title : ( The Cozero-divisor Graph of a Commutative Ring )

Authors: mozhgan afkhami goli , Kazem Khashyarmanesh ,

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For a commutative ring R with non-zero identity, we denote the set of non-zero element x in R with xR neq R by W^*(R). So W^*(R) is the set of non-units of R. In this paper, we introduced the cozero-divisor graph Gamma\\\'(R), which is a dual of zero-divisor graph Gamma(R) in some sense, as the (undirected) graph with vertices W^*(R) and for two distinct elements x and y in W^*(R), the vertices x and y are adjacent if and only if x not in R and y not in xR. We investigate the interplay between the ring-theoretic properties of R and graph-theoretic properties of Gamma\\\\\\\'(R). Also we study the relations between two graphs Gamma(R) and Gamma\\\'(R).

Keywords

, Zero-divisor graph, Complete graph, Girth,
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@article{paperid:1026654,
author = {Afkhami Goli, Mozhgan and Khashyarmanesh, Kazem},
title = {The Cozero-divisor Graph of a Commutative Ring},
journal = {Southeast Asian Bulletin of Mathematics},
year = {2011},
volume = {35},
number = {1},
month = {June},
issn = {0129-2021},
pages = {753--762},
numpages = {9},
keywords = {Zero-divisor graph; Complete graph; Girth; Diameter},
}

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%0 Journal Article
%T The Cozero-divisor Graph of a Commutative Ring
%A Afkhami Goli, Mozhgan
%A Khashyarmanesh, Kazem
%J Southeast Asian Bulletin of Mathematics
%@ 0129-2021
%D 2011

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