The First and Second Zagreb Index of Complement Graph and Its Applications of Molecular Graph

Alsharafi, Mohammed; Shubatah, Mahiuob M. Q.; Alameri, Abdu

doi:10.9734/ajpas/2020/v8i330207

Cited by 4 publications

(3 citation statements)

References 5 publications

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“…Definition 2.1. [25] The complement graph of a graph G denoted by G, is a graph on the same set of vertices V (G) in which two vertices u and v are adjacent, i.e., connected by an edge uv, if and only if they are not adjacent in G.…”

Section: Preliminariesmentioning

confidence: 99%

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

Alsharafi

Zeren

Alameri

2021

AJPAS

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In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

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Section: Preliminariesmentioning

confidence: 99%

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

Alsharafi

Zeren

Alameri

2021

AJPAS

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“…and strong product Γ 1 * Γ 2 of two undirected and connected graphs. Alsharaf et al [23][24][25] studied the frst, second, forgotten, and second hyper-Zagreb indices of some graph and complement operations on the graph. Tis paper will further explore the behavior of the Y-index for joining two connected graphs and the Y-index of the various graph operations to supplement the graph and apply the results to fnd the Y-index of some certain nanostructures.…”

Section: Introductionmentioning

confidence: 99%

The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus

Alsharafi,

Alameri,

Zeren

et al. 2024

Journal of Mathematics

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Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the Y-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the Y-polynomial of titania nanotubes and the formulae for the Y-index, Y-polynomial, F-index, F-polynomial, and Y-coindex of the HAC5C7q,p and HAC5C6C7q,p nanotubes and their molecular complement graphs have been investigated.

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“…Li and Zheng [15] introduced the first general Zagreb index in 2005, while in 2013, Shirdel and Sayadi et al [16][17][18][19] computed the Hyper-Zagreb index for certain graph operations. Wei et al [20,21] investigated the first and second Zagreb indices as well as the first and second Hyper-Zagreb Indices of Carbon Nanocones CN C k [n] in 2016. The general Rendi'c index was defined by Li and Gutman [22].…”

Section: Introductionmentioning

confidence: 99%

The Second Hyper-Zagreb Index and Coindex of Chemical Nano-structures in Drugs

Alsharafi,

Zeren,

Ahmed

et al. 2023

Preprint

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The various dendrimer nanoparticles have properties like multivalency, controlled size, and surface functionality that make them promising nanocarriers for targeted drug delivery and other applications in pharmaceutical sciences. The precise tunability of dendrimers is an advantage over other nanoparticles. The topological descriptors can be used to predict the physicochemical properties of dendrimers and optimize their branching pattern for specific applications. The second Hyper-Zagreb index and coindex were computed for various chemical structures, including dendrimers, to facilitate the correlation between their structure and biological activity. In this study, the second Hyper-Zagreb index and coindex were computed for various chemical structures, such as the molecular graph of poly(propyl) ether imine dendrimer P ET IM nanostar dendrimer (D3[p]), Polypropylenimine octaamine dendrimer (NS1[p]) and (NS2[p]), Polymer dendrimer (NS3[p]) and (NS5[p]), Fullerene dendrimer (NS4[p]), and other classes of dendrimers.

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The First and Second Zagreb Index of Complement Graph and Its Applications of Molecular Graph

Cited by 4 publications

References 5 publications

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus

The Second Hyper-Zagreb Index and Coindex of Chemical Nano-structures in Drugs

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