A note on co-maximal graphs of commutative rings

A note on co-maximal graphs of commutative rings

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Let R be a commutative ring with unity. The co-maximal graph Γ ( R ) is the graph with vertex set R and two vertices a and b are adjacent if R a + R b = R . In this paper, we characterize rings for which the co-maximal graph Γ ( R ) is a line graph of some graph G and determine rings for which Γ ( R...

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Main Authors: Deepa Sinha, Anita Kumari Rao
Format: Article
Language:English
Published: Taylor & Francis Group 2018-04-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S097286001830063X
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spelling doaj-7cf5ebd299f84b219c92291e5aa6ebe82020-11-25T03:51:11ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002018-04-01151112114A note on co-maximal graphs of commutative ringsDeepa Sinha0Anita Kumari Rao1Corresponding author.; South Asian University, New Delhi 110021, IndiaSouth Asian University, New Delhi 110021, IndiaLet R be a commutative ring with unity. The co-maximal graph Γ ( R ) is the graph with vertex set R and two vertices a and b are adjacent if R a + R b = R . In this paper, we characterize rings for which the co-maximal graph Γ ( R ) is a line graph of some graph G and determine rings for which Γ ( R ) is Eulerian or Hamiltonian. We also find the diameter and girth of Γ ( R ) . Keywords: Finite commutative ring, Maximal ideal, Co-maximal graph, Line graphhttp://www.sciencedirect.com/science/article/pii/S097286001830063X
collection DOAJ
language English
format Article
sources DOAJ
author Deepa Sinha
Anita Kumari Rao
spellingShingle Deepa Sinha
Anita Kumari Rao
A note on co-maximal graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics
author_facet Deepa Sinha
Anita Kumari Rao
author_sort Deepa Sinha
title A note on co-maximal graphs of commutative rings
title_short A note on co-maximal graphs of commutative rings
title_full A note on co-maximal graphs of commutative rings
title_fullStr A note on co-maximal graphs of commutative rings
title_full_unstemmed A note on co-maximal graphs of commutative rings
title_sort note on co-maximal graphs of commutative rings
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2018-04-01
description Let R be a commutative ring with unity. The co-maximal graph Γ ( R ) is the graph with vertex set R and two vertices a and b are adjacent if R a + R b = R . In this paper, we characterize rings for which the co-maximal graph Γ ( R ) is a line graph of some graph G and determine rings for which Γ ( R ) is Eulerian or Hamiltonian. We also find the diameter and girth of Γ ( R ) . Keywords: Finite commutative ring, Maximal ideal, Co-maximal graph, Line graph
url http://www.sciencedirect.com/science/article/pii/S097286001830063X
work_keys_str_mv AT deepasinha anoteoncomaximalgraphsofcommutativerings
AT anitakumarirao anoteoncomaximalgraphsofcommutativerings
AT deepasinha noteoncomaximalgraphsofcommutativerings
AT anitakumarirao noteoncomaximalgraphsofcommutativerings
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