Title : ( PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING )
Authors: M. Afkhami , Kazem Khashyarmanesh ,
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Abstract
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by \Gamma'(R), is a graph with vertex-set 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 Rb and b\notin Ra. In this paper, we characterize all finite commutative rings R such that \Gamma'(R) is planar, outerplanar or ring graph.
Keywords
, Outerplanarity, Cozero-divisor graph, Ring graph, Planarity
@article{paperid:1033833,
author = {M. Afkhami and Khashyarmanesh, Kazem},
title = {PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING},
journal = {Journal of Algebra and its Applications},
year = {2012},
volume = {11},
number = {6},
month = {January},
issn = {0219-4988},
pages = {1250103--12501039},
numpages = {11250936},
keywords = {Outerplanarity;Cozero-divisor graph; Ring graph; Planarity},
}
%0 Journal Article
%T PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING
%A M. Afkhami
%A Khashyarmanesh, Kazem
%J Journal of Algebra and its Applications
%@ 0219-4988
%D 2012
