Irregularity Molecular Descriptors of Hourglass, Jagged-Rectangle, and Triangular Benzenoid Systems

Hussain Hussain,Ahmad Ahmad,Munir Munir,Rafique Rafique,Athar Athar,Min Kang Min Kang,Chaudhary Chaudhary

doi:10.3390/pr7070413

Abstract

Determining the degree of irregularity of a certain molecular structure or a network has been a key source of interest for molecular topologists, but it is also important as it provides an insight into the key features used to guess properties of the structures. In this article, we are interested in formulating closed forms of irregularity measures of some popular benzenoid systems, such as hourglass H (m, n), jagged-rectangular J (m, n), and triangular benzenoid T (m, n) systems. We also compared our results graphically and concluded which benzenoid system among the above listed is more irregular than the others.

Highlights

Benzenoid hydrocarbons have consistently attracted the attention of both chemists and pure mathematicians because of the complexities of the underlying molecular graphs, combinatorically and topologically
A benzenoid system is defined to be a connected planar simple graph obtained by regular hexagons, with two such hexagons sharing a common edge or disjoint
Let h be the number of hexagons in a benzenoid system, for h = 1, we have a single, non-isomorphic benzenoid system as the single benzene molecule

Summary

Introduction

Benzenoid hydrocarbons have consistently attracted the attention of both chemists and pure mathematicians because of the complexities of the underlying molecular graphs, combinatorically and topologically. Mathematical chemistry can be useful to predict the properties of chemical compounds numbers, which collectively gather information relating to the pattern and topology of the molecular without theThe help of quantum mechanics. Benzenoid for triangular, hourglass, and jagged benzenoidissystems, from vertex These M-polynomials, systems are of greatnine importance in theoretical chemistry as In so,[10,11,12], are recently well-studied [9,10,11]. They recovered degree-based topological indicesand, in [9]. Forfamous computational aspects and analysis of different degree-based indices of some famous tubes and benzenoid systems, namely, triangular, hourglass, and jagged-rectangular benzenoid systems.

Preliminaries and Notations

Main Results

Graphical Analysis, Discussions, and Conclusions