Research Article Degree-Based Entropy for a Non-Kekulean Benzenoid Graph Md. Ashraful Alam , 1 Muhammad Usman Ghani, 2 Muhammad Kamran , 2 Muhammad Shazib Hameed, 2 Riaz Hussain Khan , 2 and A. Q. Baig 3 1 Department of Mathematics, Jahangirnagar University, Savar, Dhaka, Bangladesh 2 Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Punjab 64200, Pakistan 3 Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan Correspondence should be addressed to Md. Ashraful Alam; ashraf_math20@juniv.edu Received 13 March 2022; Revised 11 April 2022; Accepted 13 April 2022; Published 6 June 2022 Academic Editor: Hassan Raza Copyright © 2022 Md. Ashraful Alam 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. Tessellations of kekulenes and cycloarenes have a lot of potential as nanomolecular belts for trapping and transporting heavy metal ions and chloride ions because they have the best electronic properties and pore sizes. e aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties of a class of cycloarenes known as kekulenes have been the subject of several experimental and theoretical studies. rough topological computations of superaromatic structures with pores, we investigate the entropies and topological characterization of different tessellations of kekulenes. Using topological indices, the biological activity of the underlying structure is linked to its physical properties in (QSPR/QSAR) research. ere is a wide range of topological indices accessible, including degree-based indices, which are used in this work. With the total π-electron energy, these indices have a lot of iteration. In addition, we use graph entropies to determine the structural information of a non-Kekulean benzenoid graph. In this article, we study the crystal structure of non-Kekulean benzenoid graph K n and then calculate some entropies by using the degree-based topological indices. We also investigate the relationship between degree-based topological indices and degree-based entropies. is relationship is very helpful for chemist to study the physicochemical characterization of non-Kekulean benzenoid chemical. ese numerical values correlate with structural facts and chemical reactivity, biological activities, and physical properties. 1. Introduction Chemical graph theory is used to mathematically model molecules in order to review their physical properties. It is also a good idea to characterize chemical structures. Chemical graph theory could be a mathematical branch that combines graph theory and chemistry. Topological indices are molecular descriptors that can be used to describe these characteristics and specific chemical graphs [1]. e topological index of a chemical composition is a numerical value or continuation of a given structure under consideration that indicates chemical, physical, and biological properties of a chemical molecule structure [2]. It also belongs to a category of nontrivial chemical graph theory applications for exact molecular problem solutions. is theory is essential in the field of chemical sciences and chemical graph theory. More information is on quantity structure activity relationship (QSAR) and quantity struc- ture property relationship (QSPR), which are used to predict biobiota and physicochemical properties in chemical com- pounds [3, 4]. In this article, G is the connected simple chemical structure, with V(G) vertices set and E(G) edges set. Degree of any vertex u is denoted by  R(u). e edge between vertices u and v is denoted by uv. e total number of atoms linked to v j of G is denoted by d v j , and it is the atom-bond of every atom of G. If G is a graph which contains m atoms and n atom-bonds, then order of G, denoted by |G|, is m and the size of G denoted by S(G) is n. An alternating sequence of atoms and atom-bonds in a graph G is known as a path in G. Hindawi Journal of Mathematics Volume 2022, Article ID 2288207, 12 pages https://doi.org/10.1155/2022/2288207