Degree-based topological indices and QSPR analysis of Cytomegalovirus drugs

1. Introduction

Cytomegalovirus (CMV) is a type of virus that is part of the Herpesvirales order and the Herpesviridae family and the subfamily Betaherpesvirinae. These viruses are known to infect humans and other primates, and they are commonly referred to as human herpesvirus 5 (HHV-5). CMV infections can occur in various tissues and organs in the body, and they can be particularly problematic in individuals with weakened immune systems, such as transplant recipients. CMV is a widespread virus, and many people carry it without experiencing significant symptoms, but it can cause severe illness in certain circumstances. Cidofovir, Foscarnet, Ganciclovir, Maribavir, and Valganciclovir are all antiviral medications used to treat Cytomegalovirus infections.¹

Topological indices are numerical representations that encapsulate various characteristics of chemical compounds, including but not limited to, molar volume, surface tension, polarizability, polar surface area, molar refractivity, index of refraction, flashpoint, enthalpy of vaporization, vapor pressure, boiling point, and density without requiring actual lab experiments.² They are used across different domains, that is, biology, bioinformatics, and mathematics.³ However, their most notable application is in quantitative structure–property relationship (QSPR), where they are used to guess the physicochemical properties of drugs, thus eliminating the need for lab experiments.^4,5

Various graph topological indices fall into categories such as spectrum based, degree based, and spectrum based. Degree-based topological indices are particularly significant in pharmacology and theoretical chemistry. Noteworthy indices in this category include the Sum connectivity index, Harmonic index, Zagreb indices, Randić index, and others. For instance, the Randić index stands out as a valuable molecular descriptor in quantitative structure–activity relationship (QSAR) studies, offering a desirable measure for assessing the branching extent of the carbon-atom skeleton in saturated hydrocarbons.⁶

It’s been noted by researchers that a drug’s physicochemical attributes significantly affect its absorption and toxicity. There is a wealth of research exploring the link between these attributes and various facets of drug behavior, such as dissolution, absorption, and overall effectiveness. For instance, the interplay of physicochemical aspects, physical factors, and formulation on drug dissolution and absorption were emphasized in a study by Jambhekar and Breen.⁷ Müller et al.⁸ examined how physicochemical properties impact the characterization and nanosuspension’s top-down process. Similarly, Zhao et al.⁹ delved into how surface and physicochemical characteristics determine the in vivo fate of drug nanocarriers. Furthermore, a study by Ahmad et al.¹⁰ studied the antioxidant activity, drug-likeness, and physicochemical properties of oxindole derivatives.

The QSPR/QSAR investigation is a technique employed for predicting the physicochemical characteristics of chemical compounds through the utilization of topological indices. This method has been implemented in recent research to examine a range of drugs, such as resilient anticancer drugs, anti-COVID-19 medications targeted at the Omicron variant, treatments for breast cancer, assessments of entropies involving benzene derivatives, nanotube, and drugs for Lyme disease. Ivan et al. investigated the QSAR model for anti-HIV-1 activities of HEPT derivatives, employing multiple linear regression (MLR) and partial least squares (PLS).¹¹ Subsequently, Kausar and Falcao introduced a computerized framework for constructing QSAR models.¹²

Mondal et al.^13,14 delved into the connection between the physicochemical attributes of molecular graphs of chemical structures and some topological indices based on the vertex degree. They also studied the neighborhood Zagreb index of product graphs in Refs. 15 and 16. Further, they studied new degree-based topological indices in the context of COVID-19 through QSPR models in Refs. 17 and 18. In Ref. 19, topological indices were used to examine QSPR/QSAR of drugs developed for treating coronavirus disease (COVID-19). Li et al.²⁰ showed interest in resistant anticancer drugs with the help of QSPR evaluation and VIKOR multi-criteria for deciding with topological descriptors. The authors in Ref. 21 analyzed the QSPR model through Revan indices for predicting the physicochemical properties of drugs used for the treatment of the Zika virus. The physicochemical attributes of breast cancer drugs were investigated using QSPR entropy indices based on Ve-Degree in Ref. 22. In Ref. 23, Hui et al. examined the excellent check of entropies primarily based on benzene derivatives. Also, in Ref. 24, the QSPR model was applied to nanotubes through MLR analysis for operational research. Moreover, Huang et al.²⁵ carried out a QSPR evaluation of drugs used for treating Lyme disease. Shanmukha et al. in Ref. 26 calculated the entropy of porous graphene using topological indices. Using the topological indices and curve fitting method, the authors in Ref. 27 derived the physical analysis of natural cellulose network polymers.

Let $G=(V,E)$ be a graph, where $V(G)$ and $E(G)$ are the vertex set and edge set of G, respectively. If any pair of vertices of G can be connected, then G is said to be $connected$. The total number of vertices adjacent to a vertex p in G is called the $degree$ of the vertex p. It is common to denote the degree of a vertex p by $d(p)$.

While determining the $\pi$-electron energy of hydrocarbons, Gutman et al. in Ref. 28 introduced the notion of first and second Zagreb indices :

The difference of Zagreb indices has lots of chemical applications. The third Zagreb index is as follows : Due to the significant success and significance of Zagreb indices, various revised and newly discovered forms have been presented to contribute more information concerning chemical graphs.

The notion of the redefined third Zagreb index was introduced by Ranjini et al. in Ref. 29 as follows :

The reduced second Zagreb index was introduced by Furtula et al. in Ref. 30 as follows : Shirdel et al.³¹ introduced a revised form of the Zagreb index known as the hyper-Zagreb index. It is given by To find the enthalpy to form alkanes, Estrada et al.³² defined the atom bond connectivity index. Its mathematical definition is The Randić index was proposed by Randić³³ as follows : The notion of the harmonic index was introduced by Liu and Zhang in Ref. 34 as follows : In 1975, Furtula and Gutman³⁵ introduced the forgotten index. Zhou and Trinajstic³⁶ introduced the concept of Ref. 36 of the sum connectivity index. It is given by

Later in Ref. 37, Vukicevic and Gásperov introduced the concept of inverse sum index as follows :

The majority of topological indices were initially developed for examining chemical structures.^38,39,40

2. Methods and Techniques

The methods used in this paper contain the counting of the degree of vertices, division of vertices based on degree, and partitioning of edges depending on the degree of end vertices. The topological indices as given in formulas (1)–(11) are found with the help of vertex degree counting and the partition of edges technique. The JMP software is used for finding correlation coefficients. The chemical structure (both 2D and 3D) of Cytomegalovirus drugs is taken from PubChem, and molecular graphs of chemical structures are drawn using Microsoft Word.

There are eleven physicochemical properties of Cytomegalovirus drugs under consideration for the analysis. The properties are molar volume (MV), surface tension (ST), polarizability (P), polar surface area (PSA), molar refractivity (MR) index of refraction (IR), flashpoint (FP), enthalpy of vaporization (EV), vapor pressure (VP), boiling point (BP), and density (D). These properties of Cytomegalovirus drugs, as given in Table 2, are collected from ChemSpidar.

3. Chemical Structure and Molecular Graphs of Cytomegalovirus Drugs

The chemical structure and molecular graph of Cytomegalovirus drugs are shown in Fig. 1.

Since the vertices denoting hydrogen atoms do not give anything to graph isomorphism, the molecular graphs of compounds are considered without hydrogen atoms.

The graph of Cytomegalovirus drugs with vertices and edges is shown in Fig. 2.

4. Result and Discussion

The topological indices of the molecular graph of Cytomegalovirus drugs are calculated using formulas (1)–(11), as shown in Table 1.

The physical properties of Cytomegalovirus drugs are taken from ChemSpider, as shown in Table 2. However, some of the properties of Ganciclovir, such as boiling point (BP), vapor pressure (VP), enthalpy of vaporization (EV), and flashpoint (FP) are not listed in the database.

4.1. Regression model

To correlate the various physical properties of Cidofovir, Foscarnet, Ganciclovir, Maribavir, and Valganciclovir, the following equation is used :

Here, P is a physical property, A is constant, b is the regression coefficient, and TI is a topological index. The constant A and regression coefficient b are calculated from JMP software for eleven physical properties of Cytomegalovirus drugs and 12 topological indices of molecular graphs of Cytomegalovirus drugs.

Using (12), we have the following linear regression models for different topological indices.

	1. First Zagreb index $M_1(G)$:
	$\mathrm{\text{Density}}=2.2171-0.0045[M_1(G)]$
	$\mathrm{\text{Boiling point}}=467.04+1.2759[M_1(G)]$
	$\mathrm{\text{Vapor pressure}}=3.5822-0.0106[M_1(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=83.2831+0.1263[M_1(G)]$
	$\mathrm{\text{Flashpoint}}=236.2951+0.7714[M_1(G)]$
	$\mathrm{\text{Index of refraction}}=1.5205+0.0015[M_1(G)]$
	$\mathrm{\text{Molar refractivity}}=-2.5865+0.6915[M_1(G)]$
	$\mathrm{\text{Polar surface area}}=111.6305+0.2257[M_1(G)]$
	$\mathrm{\text{Polarizability}}=-1.0275+0.2742[M_1(G)]$
	$\mathrm{\text{Surface tension}}=152.49-0.7141[M_1(G)]$
	$\mathrm{\text{Molar volume}}=5.1488+1.6929[M_1(G)]$

	2. Second Zagreb index $M_2(G)$:
	$\mathrm{\text{Density}}=2.1738-0.0035[M_2(G)]$
	$\mathrm{\text{Boiling point}}=481.0430+0.9814[M_2(G)]$
	$\mathrm{\text{Vapor pressure}}=3.5822-0.0093[M_2(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=85.1389+0.0927[M_2(G)]$
	$\mathrm{\text{Flashpoint}}=244.7579+0.5933[M_2(G)]$
	$\mathrm{\text{Index of refraction}}=1.5320+0.0012[M_2(G)]$
	$\mathrm{\text{Molar refractivity}}=3.1161+0.5474[M_2(G)]$
	$\mathrm{\text{Polar surface area}}=117.8122+0.1378[M_2(G)]$
	$\mathrm{\text{Polarizability}}=1.2359+0.2170[M_2(G)]$
	$\mathrm{\text{Surface tension}}=146.8207-0.5673[M_2(G)]$
	$\mathrm{\text{Molar volume}}=19.7087+1.3345[M_2(G)]$

	3. Third Zagreb index $M_3(G)$:
	$\mathrm{\text{Density}}=2.4169-0.0302[M_3(G)]$
	$\mathrm{\text{Boiling point}}=314.533+12.5833[M_3(G)]$
	$\mathrm{\text{Vapor pressure}}=2.8866-0.0133[M_3(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=60.36+1.61[M_3(G)]$
	$\mathrm{\text{Flashpoint}}=144.1067+7.6066[M_3(G)]$
	$\mathrm{\text{Index of refraction}}=1.5421+0.0059[M_3(G)]$
	$\mathrm{\text{Molar refractivity}}=-32.2242+4.5717[M_3(G)]$
	$\mathrm{\text{Polar surface area}}=80.3306+2.5524[M_3(G)]$
	$\mathrm{\text{Polarizability}}=-12.7339+1.8104[M_3(G)]$
	$\mathrm{\text{Surface tension}}=179.1758-4.5282[M_3(G)]$
	$\mathrm{\text{Molar volume}}=-82.4605+11.9294[M_3(G)]$

	4. Redefined third Zagreb index $\mathrm{\text{Re}}M{G}_3(G)$:
	$\mathrm{\text{Density}}=2.1630-0.00067[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Boiling point}}=484.3096+0.1833[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Vapor pressure}}=3.6519-0.0019[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=85.8148+0.0166[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Flash point}}=246.734+0.1108[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Index of refraction}}=1.5371+0.000236[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Molar refractivity}}=3.8075+0.1048[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Polar surface area}}=121.9128+0.0192[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Polarizability}}=1.5145+0.0415[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Surface tension}}=146.1339-0.1087[\mathrm{\text{Re}}M{G}_3(G)]$
	$\mathrm{\text{Molar volume}}=21.3084+0.2558[\mathrm{\text{Re}}M{G}_3(G)]$

	5. Reduced second Zagreb index $R{M}_2(G)$:
	$\mathrm{\text{Density}}=2.0997-0.00914[R{M}_2(G)]$
	$\mathrm{\text{Boiling point}}=504.2274+2.4876[R{M}_2(G)]$
	$\mathrm{\text{Vapor pressure}}=3.5228-0.0284[R{M}_2(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=87.9356+0.2165[R{M}_2(G)]$
	$\mathrm{\text{Flashpoint}}=258.7749+1.5038[R{M}_2(G)]$
	$\mathrm{\text{Index of refraction}}=1.5530+0.0034[R{M}_2(G)]$
	$\mathrm{\text{Molar refractivity}}=13.6327+1.4453[R{M}_2(G)]$
	$\mathrm{\text{Polar surface area}}=125.349+0.2149[R{M}_2(G)]$
	$\mathrm{\text{Polarizability}}=5.4068+0.5729[R{M}_2(G)]$
	$\mathrm{\text{Surface tension}}=136.2189-1.5066[R{M}_2(G)]$
	$\mathrm{\text{Molar volume}}=46.2593+3.4951[R{M}_2(G)]$

	6. Hyper Zagreb index $HM(G)$:
	$\mathrm{\text{Density}}=2.2067-0.00089[HM(G)]$
	$\mathrm{\text{Boiling point}}=469.8076+0.2489[HM(G)]$
	$\mathrm{\text{Vapor pressure}}=3.6368-0.00224[HM(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=83.8491+0.0240[HM(G)]$
	$\mathrm{\text{Flashpoint}}=237.9661+0.1505[HM(G)]$
	$\mathrm{\text{Index of refraction}}=1.5250+0.000307[HM(G)]$
	$\mathrm{\text{Molar refractivity}}=-2.0384+0.1376[HM(G)]$
	$\mathrm{\text{Polar surface area}}=115.867+0.0360[HM(G)]$
	$\mathrm{\text{Polarizability}}=-0.8051+0.0545[HM(G)]$
	$\mathrm{\text{Surface tension}}=151.9746-0.41218[HM(G)]$
	$\mathrm{\text{Molar volume}}=6.4120+0.3370[HM(G)]$

	7. Atom bond connectivity index $\mathrm{\text{ABC}}(G)$:
	$\mathrm{\text{Density}}=2.23587-0.0318[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Boiling point}}=463.8914+8.8357[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Vapor pressure}}=3.6752-0.0784[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=83.2573+0.8543[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Flashpoint}}=234.3838+5.3419[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Index of refraction}}=1.5160+0.0109[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Molar refractivity}}=-4.6222+4.8003[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Polar surface area}}=108.6268+1.7379[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Polarizability}}=-1.8402+1.9037[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Surface tension}}=154.5036-4.9495[\mathrm{\text{ABC}}(G)]$
	$\mathrm{\text{Molar volume}}=0.1596+11.7512[\mathrm{\text{ABC}}(G)]$

	8. Randić index $\mathrm{\text{RI}}(G)$:
	$\mathrm{\text{Density}}=2.2510-0.0523[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Boiling point}}=457.6483+14.8104[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Vapor pressure}}=3.5315-0.1082[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=81.8719+1.5229[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Flashpoint}}=230.6092+8.9542[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Index of refraction}}=1.5086+0.0182[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Molar refractivity}}=-5.7485+7.7540[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Polar surface area}}=102.7435+3.4430[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Polarizability}}=-2.2912+3.0756[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Surface tension}}=155.6237-7.9903[\mathrm{\text{RI}}(G)]$
	$\mathrm{\text{Molar volume}}=-2.6084+18.9832[\mathrm{\text{RI}}(G)]$

	9. Harmonic index $H(G)$:
	$\mathrm{\text{Density}}=2.2304-0.05312[H(G)]$
	$\mathrm{\text{Boiling point}}=464.1833+15.0243[H(G)]$
	$\mathrm{\text{Vapor pressure}}=3.4936-0.1110[H(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=82.5837+1.5399[H(G)]$
	$\mathrm{\text{Flashpoint}}=234.56+9.0835[H(G)]$
	$\mathrm{\text{Index of refraction}}=1.5121+0.0189[H(G)]$
	$\mathrm{\text{Molar refractivity}}=-2.5904+7.8519[H(G)]$
	$\mathrm{\text{Polar surface area}}=104.0985+3.4923[H(G)]$
	$\mathrm{\text{Polarizability}}=-1.0404+3.1146[H(G)]$
	$\mathrm{\text{Surface tension}}=152.5021-8.10759[H(G)]$
	$\mathrm{\text{Molar volume}}=5.6338+19.1597[H(G)]$

	10. Forgotten index $F(G)$:
	$\mathrm{\text{Density}}=2.2378-0.00177[F(G)]$
	$\mathrm{\text{Boiling point}}=458.4385+0.5045[F(G)]$
	$\mathrm{\text{Vapor pressure}}=3.6774-0.00429[F(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=82.5055+0.0496[F(G)]$
	$\mathrm{\text{Flashpoint}}=231.0936+0.30500[F(G)]$
	$\mathrm{\text{Index of refraction}}=1.5193+0.000593[F(G)]$
	$\mathrm{\text{Molar refractivity}}=-6.9086+0.2753[F(G)]$
	$\mathrm{\text{Polar surface area}}=113.8947+0.0749[F(G)]$
	$\mathrm{\text{Polarizability}}=-2.7329+0.1091[F(G)]$
	$\mathrm{\text{Surface tension}}=156.8052-0.2836[F(G)]$
	$\mathrm{\text{Molar volume}}=-6.3032+0.6774[F(G)]$

	11. Sum connectivity index $\mathrm{\text{SCI}}(G)$:
	$\mathrm{\text{Density}}=2.2304-0.1062[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Boiling point}}=464.1848+30.048[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Vapor pressure}}=3.4936-0.2221[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=82.5839+3.0799[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Flashpoint}}=234.5609+18.1671[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Index of refraction}}=1.5121+0.0379[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Molar refractivity}}=-2.5896+15.7038[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Polar surface area}}=104.0989+9.9847[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Polarizability}}=-1.0401+6.2293[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Surface tension}}=152.5013-16.2152[\mathrm{\text{SCI}}(G)]$
	$\mathrm{\text{Molar volume}}=5.6357+38.3194[\mathrm{\text{SCI}}(G)]$

	12. Inverse sum connectivity index $\mathrm{\text{ISI}}(G)$:
	$\mathrm{\text{Density}}=2.1839-0.0182[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Boiling point}}=478.0815+5.1042[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Vapor pressure}}=3.5311-0.0442[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Enthalpy of vaporization}}=84.5386+0.4978[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Flashpoint}}=242.9659+3.0858[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Index of refraction}}=1.5273+0.0065[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Molar refractivity}}=2.5499+2.7804[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Polar surface area}}=113.7614+0.8860[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Polarizability}}=1.0066+1.1025[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Surface tension}}=147.377-2.8796[\mathrm{\text{ISI}}(G)]$
	$\mathrm{\text{Molar volume}}=18.4296+6.7726[\mathrm{\text{ISI}}(G)]$

4.2. Computation of statistical parameters

The linear models are described in Tables 3–14, where N is the sample size, A is constant, b is the regression coefficient, r is the correlation coefficient, $r^2$ is the square of the correlation coefficient, F is the calculated value of the F-ration test, and p is the significant value. The value of $p\le 0.05$ in each table indicates the significance of the results.

4.3. Computation of correlation coefficients

Table 15 indicates the values of the correlation coefficient $(r)$ of physicochemical properties of Cytomegalovirus drugs with the defined topological indices.

Based on the analysis as listed in Table 15, linear regression models that give the most promising assessment of physicochemical properties are presented in Table 16.

4.4. Comparison of actual and computed values for Cytomegalovirus drugs from linear regression models

In this section, the comparison of actual and computed values for Cytomegalovirus drugs from linear regression models of topological indices is presented.

A comparison of actual and computed values for Cytomegalovirus drugs from a linear regression model of $M_1(G)$ is shown in Table 17. Here, values in bold are of great importance and have been properly emphasized.

A comparison of actual and computed values for Cytomegalovirus drugs from a linear regression model of $M_3(G)$ is shown in Table 18. The values in bold are of great importance and have been properly emphasized.

The graphical representation of the correlation coefficients of topological indices with physicochemical properties of Cytomegalovirus drugs is shown in Figs. 3(a)–3(k).

5. Conclusion

In this research, we computed the 12 topological indices for five drugs used in treating Cytomegalovirus infections — specifically, Cidofovir, Foscarnet, Ganciclovir, Maribavir, and Valganciclovir, which are shown in Fig. 2. The correlation between these indices and eleven physicochemical properties is analyzed. The results of these calculations are presented in Table 15. Additionally, the JMP software is used to fit the linear regression model and identify the best predictor indices for each property. The results are presented in Tables 3–14. The results showed that certain topological indices had strong correlations with specific physicochemical properties.

QSPR modeling demonstrated that the $\mathrm{\text{RI}}(G)$ index is the best predictor for (D), $M_3(G)$ is the best predictor for (BP), (EV), and (FP), while $M_1(G)$ is the best predictor for (MR), (P), and (ST). The $F(G)$ is the best predictor for (MV) in linear regression models. Furthermore, no topological index displays a satisfactory correlation with vapor pressure (VP), index of refraction (IR), and polar surface area (PSA).

ORCID

H. M. Nagesh  https://orcid.org/0000-0001-9864-8937