Research Article On Neighborhood Degree-Based Topological Analysis of Polyphenylene Network Chuang Sun, 1 A. Khalid, 2 H. M. Usman, 2 A. Ahmad, 2 M. K. Siddiqui, 3 and S. A. Fufa 4 1 School of Management, WuHan Polytechnic University, Wuhan 430048, China 2 Department of Mathematics, Air University Multan Campus, Multan, Pakistan 3 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan 4 Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia Correspondence should be addressed to S. A. Fufa; samuel.asefa@aau.edu.et Received 31 December 2021; Accepted 2 February 2022; Published 21 February 2022 Academic Editor: Alessandro Lo Schiavo Copyright © 2022 Chuang Sun et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Organic compounds such as polyphenylene are very important and useful for the synthesis of many new organic compounds due to their physio-chemical properties. To ascertain these properties, one can use QSPR/QSAR methods which necessitate the computation of topological indices. e topological indices based on two newly introduced abstract notions of ev-degree and ve- degree are in practice to model numerous chemical properties as well as physical properties of organic, inorganic, hybrid, and biological compounds. In this study, we computed a certain number of topological indices for the chemical graph of poly- phenylene network which will help to model some of its physio-chemical properties. 1. Introduction e detailed critical inspection in order to discover essential features or meanings of chemical compounds graphically is known as chemical graph theory. It is the branch of mathematics, which alloys chemistry and graph theory. In graph theory, a simple graph or just graph G(V, E) is constructed by two sets: V � v 1 , ... ,v n  , the set of vertices, and E � e 1 , ... ,e m  , the set of edges. Each v ∈ V represents a node in the graph and each e ∈ E denotes the line joining two nodes. In chemical graph theory, the image obtained from diffraction of X-rays or electron microscopy of a compound (biological or chemical) is drawn into plane and lighted upon its symmetry, and then, peculiarities of this compound is mathematically modeled. e simple sketch of the image of compound is known as the chemical graph where we assume that the ends or vertices are atoms and lines or edges are the bonds between the atoms. Chemical graph theory helps to understand different properties, namely, molecular structure, kinetics of molecules, atoms or electrons, chain or patterns of polymers, crystals and clusters, aromaticity, nuclear magnetic resonance (NMR) analysis, depicting or- bitals, and electrons behaviors. Ante Graovac, Alexandru Balaban, Haruo Hosoya, Iv a ′ n Gutman, Nenad Trinajstic, and Milan Randic are few scientists who introduced graph theory in chemistry [1]. e job of mathematical modeling the properties of chemical compounds is done by topological indices which we define as a number obtained by a real-valued function, g � g(e),g � g(v)org � g(e, v), that is applied to any chemical graph (or molecular structure) of a compound to determineitstopology,isknownastopologicalgraphindexor just topological index (plural: topological indices), where e and v ∈ Z + are edges and vertices of graph, for example, Zagreb indices and their variants, distance indices, detour index, and Wiener index. ere are different kinds of to- pological indices based on degree, distance, and counting [2]. Many physical and chemical properties of different chemical and biological compounds have been modeled mathematically by the aid of topological indices such as boiling point, anti-leishmanial effect, acute toxicity, radial scavenging activity, and many more [3–5]. In this study, we considered some topological indices based on degree of Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 1951226, 14 pages https://doi.org/10.1155/2022/1951226