Abstract

In the study of the quantitative structure–activity relationship and quantitative structure-property relationships, the eccentric-connectivity index has a very important place among the other topological descriptors due to its high degree of predictability for pharmaceutical properties. In this paper, we compute the exact formulas of the eccentric-connectivity index and its corresponding polynomial, the total eccentric-connectivity index and its corresponding polynomial, the first Zagreb eccentricity index, the augmented eccentric-connectivity index, and the modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

Highlights

  • Dendrimers are synthetic polymers with highly branched structures, consisting of multiple branched monomers radiating from a central core

  • Topological indices are the mathematical measures associated with molecular graph structures that correlate a chemical structure with various physical properties, biological activities or chemical reactivities

  • A topological index is an invariant of a graph, G1 ; that is, if Top( G1 ) denotes a topological index of graph G1, and if G2 is another graph such that G1 ∼

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Summary

Introduction

Dendrimers are synthetic polymers with highly branched structures, consisting of multiple branched monomers radiating from a central core. Layers of monomers are attached stepwise during synthesis, with the number of branch points defining the generation of a dendrimer [1]. Different kinds of experiments have proved that these polymers with well-defined dimensional structures and topological architectures have an array of applications in medicine [2]. Dendrimers are currently attracting the interest of a great number of scientists because of their unusual physical and chemical properties and their wide range of potential applications in different fields, such as physics, biology, chemistry, engineering, and medicine [3]. A topological index, sometimes known as a graph theoretic index, is a numerical invariant of a chemical graph. Biochemistry and nanotechnology, distance-based topological indices of graphs are useful in isomer discrimination, structure–property relationships and structure–activity relationships

Definitions and Notations
The Eccentricity-Based Indices and Polynomials for the Molecular Graph
Conclusions
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