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Research Article Open access CC BY 4.0

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

Mohammed S. Alsharafi, Mahioub M. Shubatah, Abdu Q. Alameri

Asian Journal of Probability and Statistics · pp. 15–30 · Published 22 Aug 2020

10.9734/ajpas/2020/v8i330207

Abstract

In this paper, some basic mathematical operation for the second Zagreb indices of graph containing the join and strong product of graph operation, and the rst and second Zagreb indices of complement graph operations such as cartesian product G1 G2, composition G1 G2, disjunction G1 _ G2, symmetric dierence G1 G2, join G1 + G2, tensor product G1  G2, and strong product G1 G2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

Zagreb index Zagreb coindex complement graph graph operation.

Cited by 4

On the Reformulated Second Zagreb Index of Graph Operations

Durbar Maji, Ganesh Ghorai, Yaé Ulrich Gaba · Journal of Chemistry · 2021

Eccentricity based graph parameters of subdivision-vertex-vertex (edge-edge) join products

Anam Shahzad, Muhammad Kamran Jamil, Adel Fahad Alrasheedi · Ain Shams Engineering Journal · 2025

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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