Page | 1082 Received: 03 September 2020 Revised: 15 October 2020 Accepted: 18 October 2020 DOI: 10.22034/ecc.2020.251916.1080 Eurasian Chem. Commun. 2 (2020) 1082-1087 http:/echemcom.com FULL PAPER Weighted entropy of Zig-Zag chain Farkhanda Afzal a, * |Sidra Razaq b |Mehmoona Abdul Razaq c |Murat Cancan d |Mehmet Serif Aldemir e a MCS, National University of Sciences and Technology, Islamabad, Pakistan b Department of Mathematics, Lahore College for Women University, Jhang Campus, Jhang, Pakistan c Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan d Faculty of Education, Van Yüzüncü Yıl University, Van, Turkey e Faculty of Science, Van Yüzüncü Yıl University, Van, Turkey *Corresponding Author: Farkhanda Afzal Tel.: +92-3310046177 The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J. Krner in 1973. Although the notion of graph entropy has its roots in information theory, it was proved to be closely related to some classical and frequently studied graph theoretic concepts. In this article, we obtained the graph entropy with Randić, geometric-arithmetic, harmonic, first Zagreb, second Zagreb, atom bond connectivity, sum connectivity index and augmented Zagreb indices for Zig-Zag chain of 8-cycles molecular graph. KEYWORDS Topological indices; weighted entropy; Zig-Zag chain of 8- cycles. Introduction In medicine mathematical model, the structure of drug is represented as an undirected graph, where each vertex indicates an atom and each edge represents a chemical bond between these atoms. With prompt flourishment of manufacturing industry of medicine, hundreds and thousands of drug are produced into market every year. Hence the categorization of the biological, chemical, biochemical and pharmaceutical characteristics of these calls requires a mammoth sum of work, so this work burden has made the data and information more fastidious and clustered. To tryout the benits, performance and side effects of latest and former drugs requires a large gigantic amount of reagents, apparatus and collaboration. However, in developing and poor countries (like Pakistan, India and Africa), it is arduous to manage the expenditures and cost for appliances and reagents required for testing biochemical characteristics. By good luck, previous studies [1, 3-5] have directed the pharmacodynamic and pharmacokinetic properties of drugs and linked information of their chemical composition. It will be helpful for pharmaceutical and medical intellects to know the characteristics of medicine. It will reduce the defects of chemical experiments, if we calculate indicators of these drug molecular structure [2, 6-8] in view of defining the topological indices. For more study and research readers can see [9-26]. Some important formulas of degree based topological indices are given below: Randić index R(G)= ( ) 1 . gh E G g h d d   Reciprocal Randić index RR(G)= ( ) . g h gh E G d d   First Zagreb index M1(G)= ( ) ( ) g h gh E G d d   