Reformulated Zagreb Indices of Some Derived Graphs

Jia-Bao Liu,Bahadur Ali,Muhammad Imran,Muhammad Aslam Malik,Hafiz Muhammad Afzal Siddiqui

doi:10.3390/math7040366

Jia-Bao Liu, Bahadur Ali + Show 3 more

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https://doi.org/10.3390/math7040366

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Abstract

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

Highlights

In the fields of mathematical chemistry and chemical graph theory, a topological index is a numerical parameter that is measured based on the molecular graph of a chemical constitution.Topological indices are extensively used in the study of quantitative structure-activity relationships (QSARs) to establish the correlation between different properties of molecules and/or the biological activity with their structure
Much interest has been shown by researches and scientists in the reformulated Zagreb indices [11,12,13,14,15]
Another vertex-degree-based topological index was found to be useful in the earliest work on Zagreb indices [3,16], but later was totally ignored

Summary

Introduction

In the fields of mathematical chemistry and chemical graph theory, a topological index is a numerical parameter that is measured based on the molecular graph of a chemical constitution. We use the notations V = V ( G ) and E = E( G ) for the vertex set and edge set of G, respectively. E ∼ f indicates that the edges e and f are incident Another expression for the first reformulated Zagreb index is: EM1 = EM1 ( G ) =. Much interest has been shown by researches and scientists in the reformulated Zagreb indices [11,12,13,14,15] Another vertex-degree-based topological index was found to be useful in the earliest work on Zagreb indices [3,16], but later was totally ignored. Let, as before, G be a simple and connected graph with vertex set V ( G ) and edge set E( G ).

Reformulated First Zagreb Index of Some Derived Graphs

Reformulated Second Zagreb Index of Some Derived Graphs

Conclusions