The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices

The Cartesian product and join are two classical operations in graphs. Let [Formula: see text] be the degree of a vertex [Formula: see text] in line graph [Formula: see text] of a graph [Formula: see text]. The edge versions of atom-bond connectivity ([Formula: see text]) and geometric arithmetic ([...

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Autores principales: Zhang, Xiujun, Jiang, Huiqin, Liu, Jia-Bao, Shao, Zehui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6100620/
https://www.ncbi.nlm.nih.gov/pubmed/30012953
http://dx.doi.org/10.3390/molecules23071731
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author Zhang, Xiujun
Jiang, Huiqin
Liu, Jia-Bao
Shao, Zehui
author_facet Zhang, Xiujun
Jiang, Huiqin
Liu, Jia-Bao
Shao, Zehui
author_sort Zhang, Xiujun
collection PubMed
description The Cartesian product and join are two classical operations in graphs. Let [Formula: see text] be the degree of a vertex [Formula: see text] in line graph [Formula: see text] of a graph [Formula: see text]. The edge versions of atom-bond connectivity ([Formula: see text]) and geometric arithmetic ([Formula: see text]) indices of G are defined as [Formula: see text] and [Formula: see text] , respectively. In this paper, [Formula: see text] and [Formula: see text] indices for certain Cartesian product graphs (such as [Formula: see text] , [Formula: see text] and [Formula: see text]) are obtained. In addition, [Formula: see text] and [Formula: see text] indices of certain join graphs (such as [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text]) are deduced. Our results enrich and revise some known results.
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spelling pubmed-61006202018-11-13 The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices Zhang, Xiujun Jiang, Huiqin Liu, Jia-Bao Shao, Zehui Molecules Article The Cartesian product and join are two classical operations in graphs. Let [Formula: see text] be the degree of a vertex [Formula: see text] in line graph [Formula: see text] of a graph [Formula: see text]. The edge versions of atom-bond connectivity ([Formula: see text]) and geometric arithmetic ([Formula: see text]) indices of G are defined as [Formula: see text] and [Formula: see text] , respectively. In this paper, [Formula: see text] and [Formula: see text] indices for certain Cartesian product graphs (such as [Formula: see text] , [Formula: see text] and [Formula: see text]) are obtained. In addition, [Formula: see text] and [Formula: see text] indices of certain join graphs (such as [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text]) are deduced. Our results enrich and revise some known results. MDPI 2018-07-16 /pmc/articles/PMC6100620/ /pubmed/30012953 http://dx.doi.org/10.3390/molecules23071731 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Zhang, Xiujun
Jiang, Huiqin
Liu, Jia-Bao
Shao, Zehui
The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title_full The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title_fullStr The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title_full_unstemmed The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title_short The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
title_sort cartesian product and join graphs on edge-version atom-bond connectivity and geometric arithmetic indices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6100620/
https://www.ncbi.nlm.nih.gov/pubmed/30012953
http://dx.doi.org/10.3390/molecules23071731
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