Applied Mathematics, Volume (4), No (7), Year (2013-7) , Pages (979-985)

Title : ( On the cozero-divisor graphs of commutative rings )

Authors: mozhgan afkhami goli , Kazem Khashyarmanesh ,

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‎Let R be a commutative ring with non-zero identity‎. ‎The‎ ‎cozero-divisor graph of R, ‎denoted by \Gamma'(R), ‎is a graph‎ ‎with vertices in W^*(R), ‎which is the set of all non-zero and‎ ‎non-unit elements of R, ‎and two distinct vertices a and b in‎ W^*(R) are adjacent if and only if a\notin bR and b\notin‎ ‎aR. ‎In this paper‎, ‎we investigate some combinatorial properties‎ ‎of the cozero-divisor graphs \Gamma'(R[x]) and‎ \Gamma'(R[[x]]) such as connectivity‎, ‎diameter‎, ‎girth‎, ‎clique‎ ‎numbers and planarity‎. ‎We also study the cozero-divisor graphs of‎ ‎the direct products of two arbitrary commutative rings‎.

Keywords

, clique number‎, ‎connectivity‎, ‎cozero-divisor graph‎, ‎diameter‎, ‎direct product‎, ‎girth‎, ‎rings of Polynomials‎, ‎rings of Power
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@article{paperid:1035219,
author = {Afkhami Goli, Mozhgan and Khashyarmanesh, Kazem},
title = {On the cozero-divisor graphs of commutative rings},
journal = {Applied Mathematics},
year = {2013},
volume = {4},
number = {7},
month = {July},
issn = {2152-7385},
pages = {979--985},
numpages = {6},
keywords = {clique number‎; ‎connectivity‎; ‎cozero-divisor graph‎; ‎diameter‎; ‎direct product‎; ‎girth‎; ‎rings of Polynomials‎; ‎rings of Power series},
}

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%0 Journal Article
%T On the cozero-divisor graphs of commutative rings
%A Afkhami Goli, Mozhgan
%A Khashyarmanesh, Kazem
%J Applied Mathematics
%@ 2152-7385
%D 2013

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