Open Access

ARTICLE

Analysis of Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs

Ali Ahmad¹, Roslan Hasni^2,*, Nahid Akhter³, Kashif Elahi⁴
1 College of Computer Sciences and Information Technology, Jazan, Jazan University, Saudi Arabia
2 Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kuala Terengganu, 21030, Terengganu, Malaysia
3 Department of Mathematics, Govt. College University, Lahore, Pakistan
4 Deanship of E-learning and Information Technology, Jazan University, Jazan, Saudi Arabia
* Corresponding Author: Roslan Hasni. Email:

Computers, Materials & Continua 2022, 70(2), 2895-2904. https://doi.org/10.32604/cmc.2022.015644

Received 01 December 2020; Accepted 21 April 2021; Issue published 27 September 2021

Abstract

Chemical compounds are modeled as graphs. The atoms of molecules represent the graph vertices while chemical bonds between the atoms express the edges. The topological indices representing the molecular graph corresponds to the different chemical properties of compounds. Let be are two positive integers, and be the zero-divisor graph of the commutative ring . In this article some direct questions have been answered that can be utilized latterly in different applications. This study starts with simple computations, leading to a quite complex ring theoretic problems to prove certain properties. The theory of finite commutative rings is useful due to its different applications in the fields of advanced mechanics, communication theory, cryptography, combinatorics, algorithms analysis, and engineering. In this paper we determine the distance-based topological polynomials and indices of the zero-divisor graph of the commutative ring (for as prime numbers) with the help of graphical structure analysis. The study outcomes help in understanding the fundamental relation between ring-theoretic and graph-theoretic properties of a zero-divisor graph .

---

Keywords

Zero divisor graph; Wiener index; Hosoya polynomial; (modified) Schulz index; (modified) Schulz polynomial

---