Line graph of unit graphs associated with finite commutative rings
Abstract For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In...
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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oai:scielo:S0716-091720210004009192021-08-12Line graph of unit graphs associated with finite commutative ringsPranjali,Kumar,AmitSharma,Pooja Commutative rings Unit graph Clique Chromatic number Planarity Hamiltonian Abstract For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In this manuscript, we have studied the line graph L(G(R)) of unit graph G(R) associated with R. In the course of the investigation, several basic properties, viz., diameter, girth, clique, and chromatic number of L(G(R)) have been determined. Further, we have derived sufficient conditions for L(G(R)) to be Planar and Hamiltonian.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.4 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400919en10.22199/issn.0717-6279-4112 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Commutative rings Unit graph Clique Chromatic number Planarity Hamiltonian |
| spellingShingle |
Commutative rings Unit graph Clique Chromatic number Planarity Hamiltonian Pranjali, Kumar,Amit Sharma,Pooja Line graph of unit graphs associated with finite commutative rings |
| description |
Abstract For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In this manuscript, we have studied the line graph L(G(R)) of unit graph G(R) associated with R. In the course of the investigation, several basic properties, viz., diameter, girth, clique, and chromatic number of L(G(R)) have been determined. Further, we have derived sufficient conditions for L(G(R)) to be Planar and Hamiltonian. |
| author |
Pranjali, Kumar,Amit Sharma,Pooja |
| author_facet |
Pranjali, Kumar,Amit Sharma,Pooja |
| author_sort |
Pranjali, |
| title |
Line graph of unit graphs associated with finite commutative rings |
| title_short |
Line graph of unit graphs associated with finite commutative rings |
| title_full |
Line graph of unit graphs associated with finite commutative rings |
| title_fullStr |
Line graph of unit graphs associated with finite commutative rings |
| title_full_unstemmed |
Line graph of unit graphs associated with finite commutative rings |
| title_sort |
line graph of unit graphs associated with finite commutative rings |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2021 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400919 |
| work_keys_str_mv |
AT pranjali linegraphofunitgraphsassociatedwithfinitecommutativerings AT kumaramit linegraphofunitgraphsassociatedwithfinitecommutativerings AT sharmapooja linegraphofunitgraphsassociatedwithfinitecommutativerings |
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1718439910622363648 |