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Research Article Open access CC BY 4.0

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

Mohammed Alsharafi, Yusuf Zeren, Abdu Alameri

Asian Journal of Probability and Statistics · pp. 54–75 · Published 30 Nov 2021

10.9734/ajpas/2021/v15i430364

Abstract

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.

Zagreb index Hyper-Zagreb index Y-index Second Hyper-Zagreb index Forgotten index graph operation Titania Nanotubes V-Phenylenic Nanotube V PHX[q p] V-Phenylenic Nanotorus V PHY [m; n] complement graph

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Cited by 18

Degree-Based Topological Descriptors of Hexaphenylbenzene Molecule Graphs

Mohammed Alsharafi, Mutlu Akar, Yusuf Zeren · Polycyclic Aromatic Compounds · 2023

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

Mohammed Alsharafi, Abdu Alameri, Yusuf Zeren · Journal of Mathematics · 2024

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