International Journal of Scientific Engineering and Science Volume 4, Issue 7, pp. 47-52, 2020. ISSN (Online): 2456-7361 47 http://ijses.com/ All rights reserved M-Polynomials and Degree-Based Topological Indices of Dexamethasone, Chloroquine and Hydroxychloroquine; using in COVID-19 Riaz Hussain Khan 1* , Abdul Qudair Baig 2 , Rehana Kiran 3 , Irfan Haider 4 , Muhammad Rizwan 5 , Aamena Elahi 6 1,2,3,4,5,6 Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan *Correspondence: Email: riazsargani3 @ gmail.com Abstract— The molecular structure is base in drug making. It shows chemical and biological attributes, these attributes can be determined by topological index. In this article we extract certain topological properties of Dexamethasone, Chloroquine and Hydroxychloroquine molecular structures. We calculate M-polynomials and some connectivity indices like Randić index, Zagreb index, augmented Zagreb index, inverse sum index, harmonic index and symmetric division index of these antiviral drugs. Keywords— M-polynomial, Antiviral durgs, Zagreb index, Randić index, inverse sum index, harmonic index and symmetric division index, COVID-19. I. INTRODUCTION A cell is the base of life, but a virus not contain any cell. It can not reproduce itself, it reproduce only in the living cell with RNA. There is no drug to kill the viruses, the only our immune system is the way to fight against viruses. The antiviral drugs are used to trap it inside the cell and it from coping, to give the time to immune system for preparation against viruses. In the last month of 2019, a number of pneumonia cases were reported in Wuhan China, because of a novel coronavirus (COVID 19). Its spread rate is very high and now on 9 th July 2020, 11.9 million confirmed cases reported, 54700 deaths and 6.53 million recovered worldwide [Acc. to Wikipedia]. Effective medicine with less side effect is required on the urgent bases unless its vaccine is arrived. Here we study three drugs Dexamethasone, Chloroquine and Hydroxychloroquine. Dexamethasone can be used to cure diseases like of immune disorders, allergy, certain skin condition, respiratory issues and in cancer []. It is a steriod also use for asthma and is using in COVID 19, it reduced the death rate about 33% [1]. Chloroquine and Hydroxychloroquine are used to treat malaria. These are also used in auto-immune diseases including HIV [8]. In chemical graph theory, we study the molecular structure by using a graph. In this graph we represent atoms by vertices and bonds by edges. “Every number which is uniquely determined by a graph is called a graph invariant. These invariant of molecular graph which are used for structure-property or structure-activity correlations are usually called topological indices” [5]. Let  is combination of vertices  and edges  and   is degree of vertex  and is the number of edges incident with . For molecular structure we usually take simple undirected graph. In 2015, Klavzor et al. [2] introduced degree dependent M-polynomial, that has similar the role distance based Hosoya polynomial. In present study, we calculate distance based topological indices with the help of M-polynomials. II. BASIC DEFINITIONS AND LITERATURE REVIEW In this article,  be connected simple graph, with  vertices set and  edges set. Degree of any vertex u is   . Definition: The M-polynomial of  is [2]     ∑        where δ = min{d(v)/v ∈ V (G)} , 4 = max{d(v)/v ∈ V (G)} and m ij (G) is the edge uv ∈ E(G) s.t. {d(u),d(v)} = {i,j}. The topological index began from Wiener index, in 1945, Wiener defined them while studying alkane’s boiling point [12]. The first degree based topological index is Randi ć index which presented by Milan Randić [10] and defined as      ∑  √     Generalized Randić index is    ∑  (√    )   Inverse generalized Randić index is    ∑        The first and second Zagreb indices were defined by Gutman and Trinajstić [4,6,11] and defined as     ∑           ∑       The second modified Zagreb index defined as     ∑       