Journal of Algebra and Its Applications, ( ISI ), Volume (12), No (3), Year (2013-5) , Pages (1-18)

Title : ( The Jacobson Graph of Commutative Rings )

Authors: Ali Azimi , Ahmad Erfanian , Mohammad Farrokhi Derakhshandeh Ghouchan ,

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Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by JR, is defined as a graph with vertex set R\\J(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. We obtain some graph theoretical properties of JR including its connectivity, planarity and perfectness and we compute some of its numerical invariants, namely diameter, girth, dominating number, independence number and vertex chromatic number and give an estimate for its edge chromatic number.

Keywords

diameter; girth; connectivity; planarity; perfectness; dominating number; independence number; clique number; vertex and edge chromatic number; local
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@article{paperid:1032691,
author = {Azimi, Ali and Erfanian, Ahmad and Farrokhi Derakhshandeh Ghouchan, Mohammad},
title = {The Jacobson Graph of Commutative Rings},
journal = {Journal of Algebra and Its Applications},
year = {2013},
volume = {12},
number = {3},
month = {May},
issn = {0219-4988},
pages = {1--18},
numpages = {17},
keywords = {diameter; girth; connectivity; planarity; perfectness; dominating number; independence number; clique number; vertex and edge chromatic number; local ring.},
}

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%0 Journal Article
%T The Jacobson Graph of Commutative Rings
%A Azimi, Ali
%A Erfanian, Ahmad
%A Farrokhi Derakhshandeh Ghouchan, Mohammad
%J Journal of Algebra and Its Applications
%@ 0219-4988
%D 2013

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