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

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

doi:10.1155/2020/9057815

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

J Anal Methods Chem. 2020 Mar 26:2020:9057815. doi: 10.1155/2020/9057815. eCollection 2020.

Authors

Nazeran Idrees¹, Muhammad Jawwad Saif², Sumiya Nasir³, Fozia Bashir Farooq⁴, Asia Rauf⁵, Fareeha Ashfaq¹

Affiliations

¹ Department of Mathematics, Government College University Faisalabad, 38000 Faisalabad, Pakistan.
² Department of Applied Chemistry, Government College University Faisalabad, 38000 Faisalabad, Pakistan.
³ Core Curriculum, College of Science and Human Studies, Prince Mohammad Bin Fahd University, 34754 Khobar Dhahran, Saudi Arabia.
⁴ Department of Mathematics, Al Imam Mohammad Ibn Saud University, 11432 Riyadh, Saudi Arabia.
⁵ Department of Mathematics, Government College Women University Faisalabad, 38000 Faisalabad, Pakistan.

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.