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 .
Highlights
1 Introduction Chemical graph theory is interdisciplinary research between mathematics and chemistry that deals with chemical compounds and drugs by representing them as a graph
Characteristics of chemical compounds based on topological indices would be attractive for medical and pharmaceutical researchers
To ensure the investigations’ results, drug scientists perform the test of introduced chemical compounds and drugs
Summary
Chemical graph theory is interdisciplinary research between mathematics and chemistry that deals with chemical compounds and drugs by representing them as a graph. Characteristics of chemical compounds based on topological indices would be attractive for medical and pharmaceutical researchers. Let G(V , E) be a simple and connected graph, while the distance between two distinct vertices u, v ∈ V (G) is the number of edges in the shortest path between them, denoted as d(u, v). In 1947 Wiener [1], a chemist, illustrated the connection between organic compounds’ Physico-chemical properties and their molecular graphs index. This index is called the Wiener index, defined as:. Distance-based topological polynomials and indices of Γ (Zp2 × Zq) are broadly covered in different classes of new nanomaterial, medications, and chemical compounds with structured graphical structured analysis. To make this study useful for application-based research, some direct questions are answered to conclude the results
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