Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

The generalized hierarchical product of graphs was introduced by L. Barrière et al. in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived result...

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Main Author: Nilanjan De
Format: Article
Language:English
Published: Ptolemy Scientific Research Press 2018-11-01
Series:Open Journal of Mathematical Sciences
Subjects:
Online Access:https://openmathscience.com/computing-reformulated-first-zagreb-index-of-some-chemical-graphs-as-an-application-of-generalized-hierarchical-product-of-graphs-2/
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spelling doaj-d15e47b5dfea43d7a6d69c92b2992efe2020-11-25T02:51:56ZengPtolemy Scientific Research PressOpen Journal of Mathematical Sciences2616-49062523-02122018-11-012133835010.30538/oms2018.0039Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of GraphsNilanjan De0Department of Basic Sciences and Humanities (Mathematics), Calcutta Institute of Engineering and Management, Kolkata, IndiaThe generalized hierarchical product of graphs was introduced by L. Barrière et al. in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.https://openmathscience.com/computing-reformulated-first-zagreb-index-of-some-chemical-graphs-as-an-application-of-generalized-hierarchical-product-of-graphs-2/Topological Index; Zagreb Index; Reformulated Zagreb Index; Graph Operations; Composite graphs; Generalized Hierarchical Product.
collection DOAJ
language English
format Article
sources DOAJ
author Nilanjan De
spellingShingle Nilanjan De
Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
Open Journal of Mathematical Sciences
Topological Index; Zagreb Index; Reformulated Zagreb Index; Graph Operations; Composite graphs; Generalized Hierarchical Product.
author_facet Nilanjan De
author_sort Nilanjan De
title Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
title_short Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
title_full Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
title_fullStr Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
title_full_unstemmed Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
title_sort computing reformulated first zagreb index of some chemical graphs as an application of generalized hierarchical product of graphs
publisher Ptolemy Scientific Research Press
series Open Journal of Mathematical Sciences
issn 2616-4906
2523-0212
publishDate 2018-11-01
description The generalized hierarchical product of graphs was introduced by L. Barrière et al. in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.
topic Topological Index; Zagreb Index; Reformulated Zagreb Index; Graph Operations; Composite graphs; Generalized Hierarchical Product.
url https://openmathscience.com/computing-reformulated-first-zagreb-index-of-some-chemical-graphs-as-an-application-of-generalized-hierarchical-product-of-graphs-2/
work_keys_str_mv AT nilanjande computingreformulatedfirstzagrebindexofsomechemicalgraphsasanapplicationofgeneralizedhierarchicalproductofgraphs
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