Omega, Sadhana, and PI Polynomials of Quasi-Hexagonal Benzenoid Chain.

Nazeran Idrees,Fozia Bashir Farooq,Sumiya Nasir,Fareeha Ashfaq,Asia Rauf,Muhammad Jawwad Saif

doi:10.1155/2020/9057815

Abstract

Counting polynomials are important graph invariants whose coefficients and exponents are related to different properties of chemical graphs. Three closely related polynomials, i.e., Omega, Sadhana, and PI polynomials, dependent upon the equidistant edges and nonequidistant edges of graphs, are studied for quasi-hexagonal benzenoid chains. Analytical closed expressions for these polynomials are derived. Moreover, relation between Padmakar–Ivan (PI) index of quasi-hexagonal chain and that of corresponding linear chain is also established.

Highlights

Counting polynomials are a well-known way of expressing molecular invariants of a chemical graph in polynomial form.ese polynomials depend on chemical graph properties such as matching sets, independent sets, chromatic numbers, and equidistant edges
Topological index is a numeric quantity related to a graph which predicts the chemical properties, physical properties, and biological activity. ese invariants are used in chemical modeling, drug designing, and structural activity relations
We aim to find counting polynomials, i.e., Omega polynomial, Sadhana polynomial, and PI polynomial of quasi-hexagonal chain. ese three polynomials depend upon the distance between the edges of chemical graphs

Summary

Introduction

Counting polynomials are a well-known way of expressing molecular invariants of a chemical graph in polynomial form. Ese polynomials depend on chemical graph properties such as matching sets, independent sets, chromatic numbers, and equidistant edges. Some well-known polynomials are Hosoya polynomial, Wiener polynomial, sextet polynomial, matching polynomial, and chromatic polynomials. Many important topological indices can be derived from polynomials by directly taking their value at some point or after taking derivatives or integrals. Topological index is a numeric quantity related to a graph which predicts the chemical properties, physical properties, and biological activity. Ese invariants are used in chemical modeling, drug designing, and structural activity relations. Ese polynomials count equidistant and nonequidistant edges in a graph and are very important in prediction of physiochemical properties of a molecule.

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