Howeveri, thei clinicali trialsi fori alreadyi marketedi drugsi suchi asi lopinavir, ritonavir, hydroxychloroquine, azithromycin, (Tirumalaraju [20] ) chloroquine (ClinicalTrials.gov, n.d.), Remdesivir (Tirumalaraju [19] ) etc. alongi withi antibioticsi arei beingi evaluatedi toi treati thei secondaryi infectionsi (www.clinicaltrials.gov). Alli ofi thei drugi optionsi comei fromi experiencei treatingi SARSi, MERSi ori somei otheri newi influenzai virusi previouslyi. Thesei drugsi wouldi bei helpfuli buti thei efficacyi needsi toi bei furtheri confirmedi. Fewi COVID-19 vaccinesi arei alsoi underi clinicali trialsi suchi asi Moderna's mRNA-1273, firsti US clinicali vaccinei fundedi byi NIH's NIAID (National Institute of Allergy and Infectious Diseases) (Tirumalaraju [18] ). Thus, therei isi ani unmeti requirementi fori thei specifici anti-COVID-19 therapeuticsi toi limiti thei severityi ofi thei deadlyi diseasei.
Various clinicians and researchers are engaged in investigating and developing antivirals using different strategies combining experimental and in-silico approaches see [1, 3, 5, 7-14, 14, 16, 17, 21-23] . The replication cycle of SARS-CoV-2 can be broadly divided into three processes viral entry, viral RNA replication and lastly, viral assembly and exit from the host cell which is depicted in Figure 1 . Recent studies revealed that the genome sequence of SARS-CoV-2 is very similar to that of SARS-CoV. Recently, Qamar et.al [14] reported the following phytochemicals screened against SARS-CoV-2 3CL pro which are depicted in Figure 2 . 
Ai moleculari graphi isi ai connectedi undirectedi graphi correspondingi toi structurali formulai ofi ai chemicali compoundi, soi thati verticesi ofi thei graphi correspondi toi atomsi ofi thei moleculei andi edgesi ofi thei graphi correspondi toi thei bondsi betweeni thesei atoms.i Moleculari graphsi havei fundamentali applicationsi ini chemoinformaticsi, quantitativei structure-propertyi relationships(QSPR)i, quantitativei structure-activityi relationships(QSAR)i, virtuali screeningi ofi chemicali libraries,i andi computationali drugi design. QSPRi, QSARi andi virtuali screeningi arei basedi oni thei structure-propertyi principlei, whichi statesi thati thei physicochemicali andi biologicali propertiesi ofi chemicali compoundsi cani bei predictedi fromi theiri chemicali structurei. Onei ofi thei simplesti methodsi thati havei beeni devisedi fori correlatingi structuresi withi biologicali activitiesi ori physical-chemicali propertiesi involvei moleculari descriptorsi calledi topologicali indicesi. The example of molecular graph is depicted in Figure 3 . Since physical properties or bioactivities are expressed in numbers whereas chemical structures are discrete graphs, in order to associate graphs with numbers one has to rely on graph-theoretical invariants such as local vertex invariants, e.g. vertex degree, distance sum, etc. Hundreds of topological indices have been introduced so far.
The main aim of this study is to develop a quantitative structure property relationship between two-dimensional(2D) topological indices, calculated physicochemical parameters of phytochemicals screened against SARS-CoV-2 3CL pro . Experimental data used in this study were taken from [14] . In this paper we have considered five topological indices viz., the first Zagreb index M 1 (G) [6] , the second Zagreb index M 2 (G) [6] , Randić index R(G) [15] , Balban index J(G) [2, 3] and the sum-connectivity index SCI(G) [25] . The formulae for these topological indices are give below:
where w(u) (resp. w(v)) denotes the sum of distances from u (resp. v) to all the other vertices of G.
The productivity of the above mentioned topological indices were tested using a data set of phytochemical, found at [2] and https://pubchem.ncbi.nlm.nih.gov/. The data set consists of the following data: docking score, binding affinity, molecular weight and topological polar surface, which is given in Table 1 . Note: The molecular weight and topological polar surface of NPACT00105 could not find. Therefore, we do not include this molecule for QSPR-analysis.
The topological indices values of phytochemical structures ate given in Table 2 . 
The following regression models have been used for the study: 
The QSPR study has revealed that the molecular descriptors are best candidates to predict the physicochemical properties of phyctochemicals. In particular, the sum-connectivity index (SCI) and the first Zagreb index (M 1 ) are two important parameters to predict the molecular weight and the topological polar surface area of phytochemicals respectively. Our study may help the researchers in the field of lifescience in finding the anti-covid-19 drugs.