Computation of Topological Indices of Some Special Graphs

Mohammed Salaheldeen Abdelgader,Sarra Abdalrhman Mohammed,Chunxiang Wang

doi:10.3390/math6030033

Mohammed Salaheldeen Abdelgader, Sarra Abdalrhman Mohammed + Show 1 more

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https://doi.org/10.3390/math6030033

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Abstract

There are several chemical indices that have been introduced in theoretical chemistry to measure the properties of molecular topology, such as distance-based topological indices, degree-based topological indices and counting-related topological indices. Among the degree-based topological indices, the atom-bond connectivity ( A B C ) index and geometric–arithmetic ( G A ) index are the most important, because of their chemical significance. Certain physicochemical properties, such as the boiling point, stability and strain energy, of chemical compounds are correlated by these topological indices. In this paper, we study the molecular topological properties of some special graphs. The indices ( A B C ) , ( A B C 4 ) , ( G A ) and ( G A 5 ) of these special graphs are computed.

Highlights

Graph theory, as applied in the study of molecular structures, represents an interdisciplinary science called chemical graph theory or molecular topology
By using tools taken from graph theory, set theory and statistics, we attempt to identify structural features involved in structure–property activity relationships
Topological indices are designed on the grounds of the transformation of a molecular graph into a number that characterizes the topology of the molecular graph

Summary

Introduction

As applied in the study of molecular structures, represents an interdisciplinary science called chemical graph theory or molecular topology. By using tools taken from graph theory, set theory and statistics, we attempt to identify structural features involved in structure–property activity relationships. Molecules and modeling unknown structures can be classified by the topological characterization of chemical structures with desired properties. The topological index is a numeric quantity associated with chemical constitutions purporting the correlation of chemical structures with many physicochemical properties, chemical reactivity or biological activity. Topological indices are designed on the grounds of the transformation of a molecular graph into a number that characterizes the topology of the molecular graph. We study the relationship between the structure, properties, and activity of chemical compounds in molecular modeling. Molecules and molecular compounds are often modeled by molecular graphs

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