Reformulated First Zagreb Index of Some Graph Operations

De, Nilanjan; Nayeem, Sk. Md. Abu; Pal, Anita

doi:10.3390/math3040945

Cited by 22 publications

(16 citation statements)

References 25 publications

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“…Bounds on the total multiplicative sum Zagreb index and first multiplicative sum Zagreb coindex for unicyclic and bicyclic graphs were presented by Božović, Vukićević and Popivoda [8]. Reformulated Zagreb indices were investigated Liu et al [9] and De, Nayeem and Pal [10].…”

Section: Introductionmentioning

confidence: 99%

General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

2020

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We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tricyclic graphs, tetracyclic graphs and graphs of given order, size and number of pendant vertices. We show that all our bounds are sharp by presenting extremal graphs including graphs with symmetries. Bounds for the classical multiplicative Zagreb indices are special cases of our results.

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Section: Introductionmentioning

confidence: 99%

General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

2020

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“…In [21], the Wiener index of Cartesian product graphs are studied. The present author [22][23][24] studied F-index, F-coindex and reformulated first Zagreb index for Cartesian product graphs. The goal of this work is to obtain the reduced second Zagreb index of Cartesian product graphs.…”

Section: Introductionmentioning

confidence: 99%

Reduced second Zagreb index of product graphs

De¹

2020

Nanosystems: Phys. Chem. Math.

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The reduced second Zagreb index of a graph G is defined as RM 2 (G) = uv∈E(G) (d G (u) − 1)(d G (v) − 1), where d G (v) denotes the degree of the vertex v of graph G. Recently Furtula et al. (Furtula B., Gutman I., Ediz S. Discrete Appl. Math., 2014) characterized the maximum trees with respect to reduced second Zagreb index. The aim of this paper is to compute reduced second Zagreb index of the Cartesian product of k (≥ 2) number of graphs and hence as a consequence the reduced second Zagreb index of some special graphs applicable in various real world problems are computed. Topological properties of different nanomaterials like nanotube, nanotorus etc. are studied here graphically in terms of the aforesaid aforementioned index.

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“…Ji et al in [8] and [9], computed these indices for acyclic, unicyclic, bicyclic and tricyclic graphs. Recently De et al [10], investigate reformulated first Zagreb index of various graph operations.…”

Section: Introductionmentioning

confidence: 99%

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

De¹

2018

Open J. Math. Sci

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The generalized hierarchical product of graphs was introduced by L. Barriére 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.

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Reformulated First Zagreb Index of Some Graph Operations

Cited by 22 publications

References 25 publications

General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

Reduced second Zagreb index of product graphs

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

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