Mathematical Notes, Volume (98), No (5), Year (2015-6) , Pages (813-819)

Title : ( Classification of finite commutative rings with planar, Toroidal, and projective line graphs associated with jacobson graphs )

Authors: Atossa Parsapour , Kazem Khashyarmanesh , M. Afkhami , Khadijeh Ahmad Javaheri ,

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Let R be a commutative ring with nonzero identity and J(R) be the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is a graph with vertex-set R \ J(R), such that two distinct vertices a and b in R \ J(R) are adjacent if and only if 1 − ab is not a unit of R. Also, the line graph of the Jacobson graph is denoted by L(JR). In this paper, we characterize all finite commutative rings R such that the graphs L(JR) are planar, toroidal or projective.

Keywords

, Jacobson graph, line graph, planar graph, projective graph, toroidal
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@article{paperid:1054711,
author = {Parsapour, Atossa and Khashyarmanesh, Kazem and M. Afkhami and Ahmad Javaheri, Khadijeh},
title = {Classification of finite commutative rings with planar, Toroidal, and projective line graphs associated with jacobson graphs},
journal = {Mathematical Notes},
year = {2015},
volume = {98},
number = {5},
month = {June},
issn = {0001-4346},
pages = {813--819},
numpages = {6},
keywords = {Jacobson graph; line graph; planar graph; projective graph; toroidal graph.},
}

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%0 Journal Article
%T Classification of finite commutative rings with planar, Toroidal, and projective line graphs associated with jacobson graphs
%A Parsapour, Atossa
%A Khashyarmanesh, Kazem
%A M. Afkhami
%A Ahmad Javaheri, Khadijeh
%J Mathematical Notes
%@ 0001-4346
%D 2015

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