TY  - EJOU
AU  - Ahmad, Ali 
AU  - Hasni, Roslan 
AU  - Akhter, Nahid 
AU  - Elahi, Kashif 

TI  - Analysis of Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs
T2  - Computers, Materials \& Continua

PY  - 2022
VL  - 70
IS  - 2
SN  - 1546-2226

AB  - 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 .
KW  - Zero divisor graph; Wiener index; Hosoya polynomial; (modified) Schulz index; (modified) Schulz polynomial

DO  - 10.32604/cmc.2022.015644