# Ve-Degree, Ev-Degree, and Degree-Based Topological Indices of Fenofibrate

Authors: Sadik Delen; Riaz Hussain Khan; Muhammad Kamran; Nadeem Salamat; A. Q. Baig; Ismail Naci Cangul; M. K. Pandit
Journal: Journal of Mathematics
 (2022)

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## Abstract

The molecular topology of a graph is described by topological indices, which are numerical measures. In theoretical chemistry, topological indices are numerical quantities that are used to represent the molecular topology of networks. These topological indices can be used to calculate several physical and chemical properties of chemical compounds, such as boiling point, entropy, heat generation, and vaporization enthalpy. Graph theory comes in handy when looking at the link between certain topological indices of some derived graphs. In the ongoing research, we determine ve-degree, ev-degree, and degree-based (D-based) topological indices of fenofibrate’s chemical structure. These topological indices are the Zagreb index, general Randić index, modified Zagreb index, and forgotten topological index. These indices are very helpful to study the characterization of the given structure.


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## Body

## 1. Introduction

Graph theory is a mathematical subfield. It begins in 1736 with the Konigsberg bridge problem when Leonhard Euler publish his work on the seven bridges of the city Konigsberg. Graph theory is widely used in the study of networks, models, circuits, routes, etc.. This theory has found significant applications in computing, chemistry, physics, electricity and civil engineering, communication science, operations research, architecture, genetics, sociology, psychology, anthropology, linguistics, and economics. It is mostly used in organic chemistry and is called chemistry graph theory. Graph theory is based on vertices and edges; in chemical graph theory, vertices represent items and edges represent bonding. In graph theory, we understand the terms of quantitative structure-property relation (QSAR) and quantitative structure-activity relation (QSPR) for structure or formula of compound. Topological indices are numerical values associated with a chemical structure and are used to correlate a chemical structure with many properties such as chemical stability, pharmacological activity, and physical properties. They are developed from molecular topology modeling and are divided into explicit structural descriptions such as chemical quantum and hidden structural descriptors such as hydrophobicity and electrical constants. The class of fenofibrate is referred to as antilipemic agents. It increases the natural processes to remove bad cholesterol from body. It decreases the fatty substances which are bad and also helps the fatty substances which are good for human body and reduces the risk of heart disease. Cholesterol has benefits when it remains in limit level, but when it increases from its level, it becomes a danger for the heart. In cholesterol, there are three main fats, low-density lipoprotein (LDL) and triglyceride are bad when increased but high-density lipoprotein (HDL) is known as good cholesterol. Fenofibrate is used to reduce LDL and triglyceride levels along with a low-fat diet and exercise. The main purpose of our research is to control the heart disease with the help of fenofibrate using topological index. We calculate the formula via ve-degree, ev-degree, and degree-based topological indices. In chemical graph theory, vertices represent atoms and edges represent bonding. The graph of a chemical structure is a simple undirected graph. A graph is a combination of nonempty setsℷ and Ξ. The members are vertices and edges, respectively. δℸ is the degree of vertex ℸ and is the number of edges incident to ℸ. The set of vertices which are connected to ℸ is open neighborhood of ℸ, denoted by Nℸ. Nℸ+ℸ are the closed neighborhoods of ℸ. A topological index is a unique number that defines the underlying structure of the molecular graph. These topological indices are used to study the quantitative structure-property and relationships. Scientists use the numerical parameters which are obtained from chemical graph network in QSPR and QSAR. In drug designs, its applications are in. The concept of topological index was firstly introduced by Wiener, and it was distance-based topological index. Later in 1972–75, D-based Zagreb index and Randić index were introduced. Recently, Chellali et al. [4] proposed two new degree concepts in topological indices, called ve-degree and ev-degree. Math concepts are discussed in [5]. The classical degree concepts (see [6–8]) have been converted to ve-degree and ev-degree such as Zagreb index, Randić index, modified Zagreb index, inverse degree index, and forgotten index (see [9–11]). It was found that they give better prediction results than classical indices [12, 13].


### 1.1. Motivation

In the last two years, COVID-19 has surged dramatically in numerous nations. Many pharmacists produced a variety of medications to aid in the management of COVID-19. Fenofibrate is a substance that is found in various anti-COVID-19 medications. In laboratories, studying its physicochemical properties is highly expensive and time consuming. We work on it and derive the mathematical equation utilising topological indices that are useful to chemists in order to improve it.


## 1.1. Motivation

In the last two years, COVID-19 has surged dramatically in numerous nations. Many pharmacists produced a variety of medications to aid in the management of COVID-19. Fenofibrate is a substance that is found in various anti-COVID-19 medications. In laboratories, studying its physicochemical properties is highly expensive and time consuming. We work on it and derive the mathematical equation utilising topological indices that are useful to chemists in order to improve it.


## 2. Preliminaries

Here we give basic concepts. Consider a graphΔ with ℷ vertex set and Ξ edge set. The degree is the number of edges incident to vertex ℸ, denoted as δℸ. The ve-degree of vertex ℸ is the number of edges which are incident to any vertex of close neighborhood of ℸ, denoted by δveℸ. The number of vertices in the union of closed neighborhoods of ℸ and ℷ is the ev-degree of edge e=ℸℷ, denoted by δeve.The first Zagreb index [14] introduced in 1972 is defined as(1)M1Δ=∑ℷ∈Vδℷ2=∑ℸℷ∈Ξδℸ+δℷ.The ve-degree Zagreb beta index of graphΔ is defined as(2)MβveΔ=∑ℸℷ∈Vδveℸ+δveℸ.The ve-degree Zagreb alpha index ofΔ is defined as(3)MαveΔ=∑ℷ∈Vδveℷ2.The ev-degree Zagreb index is defined as(4)MevΔ=∑e∈Ξδeve2.The Randić index [15] is defined as(5)RΔ=∑ℸℷ∈Ξδℸ×δℷ−1/2.The ve-degree Randić index of graphΔ is defined as(6)RveΔ=∑ℷ∈Vδveℷ−1/2.The ev-degree Randić index is defined as(7)RevΔ=∑e∈Ξδeve−1/2.The ve-degree modified Zagreb index is defined as(8)MmveΔ=∑ℷ∈V1δveℷ2.The ev-degree modified Zagreb index of graphΔ is defined as(9)MmevΔ=∑e∈Ξ1δeve2.TheF index [16] is defined as(10)FΔ=∑ℷ∈Vδℷ3=∑ℸℷ∈Ξδℸ2+δℷ2.The ve-degreeF index is defined as(11)F1veΔ=∑ℷ∈Vδveℷ3.The ev-degreeF index of graph Δ is defined as(12)F1evΔ=∑e∈Ξdeve3.


### 2.1. Applications of Topological Indices

Wiener created the idea of topology index while investigating alkane boiling points. Topological indices are used to studies the quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) to compare the topological similarities of different chemical compounds. Randić index has been closely correlated with many chemical properties, but the GA index is better than Randić connectivity index. Topological indices encode information regarding molecular size, shape, branching, and so on in numerical form, which is used for measuring topological similarity between chemical compounds and in (QSPR)/(QSAR) studies. Randić index has been closely correlated with many chemical properties and found to parallel the boiling point and Kovats constants. For certain physicochemical properties, the predictive power of GA index is somewhat better than predictive power of the Randić connectivity index.


## 2.1. Applications of Topological Indices

Wiener created the idea of topology index while investigating alkane boiling points. Topological indices are used to studies the quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) to compare the topological similarities of different chemical compounds. Randić index has been closely correlated with many chemical properties, but the GA index is better than Randić connectivity index. Topological indices encode information regarding molecular size, shape, branching, and so on in numerical form, which is used for measuring topological similarity between chemical compounds and in (QSPR)/(QSAR) studies. Randić index has been closely correlated with many chemical properties and found to parallel the boiling point and Kovats constants. For certain physicochemical properties, the predictive power of GA index is somewhat better than predictive power of the Randić connectivity index.


## 3. Methods

To calculate results, we use the vertex segment technique, edge partition technique, degree checking technique, and degree of neighbors strategy. We use Maple 16 for verification of calculations.


### 3.1. FenofibrateC20H21ClO4⋅2D Structure

The2D molecular graph of fenofibrate is given in Figure 1. For the computation of above given formulas for fenofibrate C20H21ClO4, we use a unit cell. To find topological indices, we partitioned edges. There are 5ℸℷ edges in the first edge division, where δℸ=1 and δℷ=3. There are 2ℸℷ edges in second edge division, where δℸ=1 and δℷ=4. There are 4ℸℷ edges in the third edge division, where δℸ=2 and δℷ=2. There are 11ℸℷ edges in the fourth edge division, where δℸ=2 and δℷ=3. There is 1ℸℷedge in the fifth edge division, where δℸ=2 and δℷ=4. There are 2ℸℷ edges in the sixth edge division, where δℸ=3 and δℷ=3. There is 1ℸℷedge in the seventh edge division, where δℸ=3 and δℷ=4. Table 1 shows the edge partition of fenofibrate.Figure 1
2D and 3D structures of fenofibrate.Table 1
Edge division of fenofibrate.
δℸ,δℷ1,31,42,22,32,43,33,4Edge partitionΞ1ΔΞ2ΔΞ3ΔΞ4ΔΞ5ΔΞ6ΔΞ7ΔFrequency52411121The molecular graph of fenofibrate is shown in Figure2.Figure 2
2D and 3D structures of fenofibrate.


### 3.2. Proof of the Topological Indices

#### 3.2.1.D-Based Zagreb Index

We calculate degree-based Zagreb index using Table1.(13)M1Δ=∑ℸℷ∈ΞΔδℸ+δℷ=51+3+21+4+42+2+112+3+2+4+23+3+3+4=126.


#### 3.2.2. Ev-D-Based Zagreb Index

We calculate ev-degree Zagreb index using Table2.(14)MevΔ=∑e∈ΞΔδeve2=8×42+13×52+3×62+72=610.Table 2
Ev-degree of fenofibrate.
δℸ,δℷEv-degreeFrequency1,3451,4522,2442,35112,4613,3623,471


#### 3.2.3. Ve-Degree-Based Zagreb Index

Using Table3, we calculate ve-degree Zagreb alpha indices.Table 3
Numerical calculations ofTIs for fenofibrate.
Topological indicesD-basedVe-degreeEv-degreeM1Δ126Mα=684/Mβ=286610R1Δ1437911.22R1/2Δ59.897141.02955.064R−1/2Δ11.6864.97511.417R−1Δ5.4310.9925.243MmΔ10.341.281.124FΔ340F1=3942/F=16623128Zagreb alpha index:(15)M1αveΔ=∑ℷ∈VΔδveℷ2=532+242+852+62+72+42+52+62+472+72=684.Zagreb beta index can be calculated by using Table4.(16)M1βveΔ=∑ℸℷ∈ΞΔδℸ+δℷ=23+4+3+5+23+7+4+6+24+7+65+5+25+6+45+7+26+7+47+7=286.Table 4
Ve-degree of end vertex of each edge of fenofibrate.
δℸ,δℷVe-degreeFrequency1,33,421,33,511,33,721,44,722,25,542,34,612,35,522,35,622,35,742,36,722,47,713,37,723,47,71


#### 3.2.4.D-Based General Randić Index

Using Table1, we calculate D-based general Randić index(17)RαΔ=∑ℸℷ∈ΞΔδℸ×δℷα=51+3α+21+4α+42+2α+112+3α+2+4α+23+3α+3+4α.Table 5
Vertex degree and corresponding frequency.
δℸTotal vertex172103741Table 6
Ve-degree of fenofibrate.
δℸVe-degreeFrequency135142258261271341351361374471Forα=1,(18)R1Δ=143.Forα=1/2,(19)R1/2Δ=59.8972.Forα=−1/2,(20)R−1/2Δ=11.6864.Forα=−1,(21)R−1Δ=5.4306.


#### 3.2.5. Ev-D-Based General Randić Index

Using Table2, we calculate D-based general Randić index:(22)RαevΔ=∑e∈ΞΔδeveα=8×4α+13×5α+3×6α+7α.Forα=1,(23)R1Δ=122.Forα=1/2,(24)R1/2Δ=55.064.Forα=−1/2,(25)R−1/2Δ=11.417.Forα=−1,(26)R−1Δ=5.2429.


#### 3.2.6. Ve-Degree-Based General Randić Index

Using Table4, we calculate ve-degree general Randić index:(27)RαveΔ=∑ℸℷ∈ΞΔδℸ+δℷα=23+4α+3+5α+23+7α+4+6α+24+7α+65+5α+25+6α+45+7α+26+7α+47+7α.Forα=1,(28)R1Δ=791.Forα=1/2,(29)R1/2Δ=141.0286.Forα=−1/2,(30)R−1/2Δ=4.9754.Forα=−1,(31)R−1Δ=0.9919.


#### 3.2.7.D-Based Modified Zagreb Index

Using Table5, we calculate D-based modified Zagreb index(32)MmΔ=∑ℷ∈VΔ1δℷ2=7+1022+732+142=10.34.


#### 3.2.8. Ev-D-Based Modified Zagreb Index

Using Table2, we calculate ev-degree modified Zagreb index:(33)MmevΔ=∑e∈ΞΔ1δeve2=8×142+13×152+3×162+172=1.1237.


#### 3.2.9. Ve-Degree-Based Modified Zagreb Index

Using Table4, we calculate ve-degree modified Zagreb index(34)MmveΔ=∑ℷ∈VΔ1δveℷ2=532+242+852+162+172+142+152+162+472+172=1.28.


#### 3.2.10.D-Based F Index

Using Table5, we calculate D-based F index(35)FΔ=∑ℷ∈VΔδℷ3=7+1023+733+43=340.


#### 3.2.11. Ev-D-Based F Index

Using Table2, we calculate ev-degree F index(36)F1evΔ=∑e∈ΞΔδeve3=8×43+13×53+3×63+73=3128.


#### 3.2.12. Ve-Degree-BasedF Index

Using Table6, we calculate ve-degree F index(37)F1veΔ=∑ℷ∈VΔδveℷ3=533+243+853+63+73+43+53+63+473+73=3942.In Figure3, all the derived indices are shown in the graphical ways. The different behaviors of the indices can be seen in the figure. In table 3 results of these TIs are given.Figure 3
Graphical analysis of the topological indices.


## 3.1. FenofibrateC20H21ClO4⋅2D Structure

The2D molecular graph of fenofibrate is given in Figure 1. For the computation of above given formulas for fenofibrate C20H21ClO4, we use a unit cell. To find topological indices, we partitioned edges. There are 5ℸℷ edges in the first edge division, where δℸ=1 and δℷ=3. There are 2ℸℷ edges in second edge division, where δℸ=1 and δℷ=4. There are 4ℸℷ edges in the third edge division, where δℸ=2 and δℷ=2. There are 11ℸℷ edges in the fourth edge division, where δℸ=2 and δℷ=3. There is 1ℸℷedge in the fifth edge division, where δℸ=2 and δℷ=4. There are 2ℸℷ edges in the sixth edge division, where δℸ=3 and δℷ=3. There is 1ℸℷedge in the seventh edge division, where δℸ=3 and δℷ=4. Table 1 shows the edge partition of fenofibrate.Figure 1
2D and 3D structures of fenofibrate.Table 1
Edge division of fenofibrate.
δℸ,δℷ1,31,42,22,32,43,33,4Edge partitionΞ1ΔΞ2ΔΞ3ΔΞ4ΔΞ5ΔΞ6ΔΞ7ΔFrequency52411121The molecular graph of fenofibrate is shown in Figure2.Figure 2
2D and 3D structures of fenofibrate.


## 3.2. Proof of the Topological Indices

### 3.2.1.D-Based Zagreb Index

We calculate degree-based Zagreb index using Table1.(13)M1Δ=∑ℸℷ∈ΞΔδℸ+δℷ=51+3+21+4+42+2+112+3+2+4+23+3+3+4=126.


### 3.2.2. Ev-D-Based Zagreb Index

We calculate ev-degree Zagreb index using Table2.(14)MevΔ=∑e∈ΞΔδeve2=8×42+13×52+3×62+72=610.Table 2
Ev-degree of fenofibrate.
δℸ,δℷEv-degreeFrequency1,3451,4522,2442,35112,4613,3623,471


### 3.2.3. Ve-Degree-Based Zagreb Index

Using Table3, we calculate ve-degree Zagreb alpha indices.Table 3
Numerical calculations ofTIs for fenofibrate.
Topological indicesD-basedVe-degreeEv-degreeM1Δ126Mα=684/Mβ=286610R1Δ1437911.22R1/2Δ59.897141.02955.064R−1/2Δ11.6864.97511.417R−1Δ5.4310.9925.243MmΔ10.341.281.124FΔ340F1=3942/F=16623128Zagreb alpha index:(15)M1αveΔ=∑ℷ∈VΔδveℷ2=532+242+852+62+72+42+52+62+472+72=684.Zagreb beta index can be calculated by using Table4.(16)M1βveΔ=∑ℸℷ∈ΞΔδℸ+δℷ=23+4+3+5+23+7+4+6+24+7+65+5+25+6+45+7+26+7+47+7=286.Table 4
Ve-degree of end vertex of each edge of fenofibrate.
δℸ,δℷVe-degreeFrequency1,33,421,33,511,33,721,44,722,25,542,34,612,35,522,35,622,35,742,36,722,47,713,37,723,47,71


### 3.2.4.D-Based General Randić Index

Using Table1, we calculate D-based general Randić index(17)RαΔ=∑ℸℷ∈ΞΔδℸ×δℷα=51+3α+21+4α+42+2α+112+3α+2+4α+23+3α+3+4α.Table 5
Vertex degree and corresponding frequency.
δℸTotal vertex172103741Table 6
Ve-degree of fenofibrate.
δℸVe-degreeFrequency135142258261271341351361374471Forα=1,(18)R1Δ=143.Forα=1/2,(19)R1/2Δ=59.8972.Forα=−1/2,(20)R−1/2Δ=11.6864.Forα=−1,(21)R−1Δ=5.4306.


### 3.2.5. Ev-D-Based General Randić Index

Using Table2, we calculate D-based general Randić index:(22)RαevΔ=∑e∈ΞΔδeveα=8×4α+13×5α+3×6α+7α.Forα=1,(23)R1Δ=122.Forα=1/2,(24)R1/2Δ=55.064.Forα=−1/2,(25)R−1/2Δ=11.417.Forα=−1,(26)R−1Δ=5.2429.


### 3.2.6. Ve-Degree-Based General Randić Index

Using Table4, we calculate ve-degree general Randić index:(27)RαveΔ=∑ℸℷ∈ΞΔδℸ+δℷα=23+4α+3+5α+23+7α+4+6α+24+7α+65+5α+25+6α+45+7α+26+7α+47+7α.Forα=1,(28)R1Δ=791.Forα=1/2,(29)R1/2Δ=141.0286.Forα=−1/2,(30)R−1/2Δ=4.9754.Forα=−1,(31)R−1Δ=0.9919.


### 3.2.7.D-Based Modified Zagreb Index

Using Table5, we calculate D-based modified Zagreb index(32)MmΔ=∑ℷ∈VΔ1δℷ2=7+1022+732+142=10.34.


### 3.2.8. Ev-D-Based Modified Zagreb Index

Using Table2, we calculate ev-degree modified Zagreb index:(33)MmevΔ=∑e∈ΞΔ1δeve2=8×142+13×152+3×162+172=1.1237.


### 3.2.9. Ve-Degree-Based Modified Zagreb Index

Using Table4, we calculate ve-degree modified Zagreb index(34)MmveΔ=∑ℷ∈VΔ1δveℷ2=532+242+852+162+172+142+152+162+472+172=1.28.


### 3.2.10.D-Based F Index

Using Table5, we calculate D-based F index(35)FΔ=∑ℷ∈VΔδℷ3=7+1023+733+43=340.


### 3.2.11. Ev-D-Based F Index

Using Table2, we calculate ev-degree F index(36)F1evΔ=∑e∈ΞΔδeve3=8×43+13×53+3×63+73=3128.


### 3.2.12. Ve-Degree-BasedF Index

Using Table6, we calculate ve-degree F index(37)F1veΔ=∑ℷ∈VΔδveℷ3=533+243+853+63+73+43+53+63+473+73=3942.In Figure3, all the derived indices are shown in the graphical ways. The different behaviors of the indices can be seen in the figure. In table 3 results of these TIs are given.Figure 3
Graphical analysis of the topological indices.


## 3.2.1.D-Based Zagreb Index

We calculate degree-based Zagreb index using Table1.(13)M1Δ=∑ℸℷ∈ΞΔδℸ+δℷ=51+3+21+4+42+2+112+3+2+4+23+3+3+4=126.


## 3.2.2. Ev-D-Based Zagreb Index

We calculate ev-degree Zagreb index using Table2.(14)MevΔ=∑e∈ΞΔδeve2=8×42+13×52+3×62+72=610.Table 2
Ev-degree of fenofibrate.
δℸ,δℷEv-degreeFrequency1,3451,4522,2442,35112,4613,3623,471


## 3.2.3. Ve-Degree-Based Zagreb Index

Using Table3, we calculate ve-degree Zagreb alpha indices.Table 3
Numerical calculations ofTIs for fenofibrate.
Topological indicesD-basedVe-degreeEv-degreeM1Δ126Mα=684/Mβ=286610R1Δ1437911.22R1/2Δ59.897141.02955.064R−1/2Δ11.6864.97511.417R−1Δ5.4310.9925.243MmΔ10.341.281.124FΔ340F1=3942/F=16623128Zagreb alpha index:(15)M1αveΔ=∑ℷ∈VΔδveℷ2=532+242+852+62+72+42+52+62+472+72=684.Zagreb beta index can be calculated by using Table4.(16)M1βveΔ=∑ℸℷ∈ΞΔδℸ+δℷ=23+4+3+5+23+7+4+6+24+7+65+5+25+6+45+7+26+7+47+7=286.Table 4
Ve-degree of end vertex of each edge of fenofibrate.
δℸ,δℷVe-degreeFrequency1,33,421,33,511,33,721,44,722,25,542,34,612,35,522,35,622,35,742,36,722,47,713,37,723,47,71


## 3.2.4.D-Based General Randić Index

Using Table1, we calculate D-based general Randić index(17)RαΔ=∑ℸℷ∈ΞΔδℸ×δℷα=51+3α+21+4α+42+2α+112+3α+2+4α+23+3α+3+4α.Table 5
Vertex degree and corresponding frequency.
δℸTotal vertex172103741Table 6
Ve-degree of fenofibrate.
δℸVe-degreeFrequency135142258261271341351361374471Forα=1,(18)R1Δ=143.Forα=1/2,(19)R1/2Δ=59.8972.Forα=−1/2,(20)R−1/2Δ=11.6864.Forα=−1,(21)R−1Δ=5.4306.


## 3.2.5. Ev-D-Based General Randić Index

Using Table2, we calculate D-based general Randić index:(22)RαevΔ=∑e∈ΞΔδeveα=8×4α+13×5α+3×6α+7α.Forα=1,(23)R1Δ=122.Forα=1/2,(24)R1/2Δ=55.064.Forα=−1/2,(25)R−1/2Δ=11.417.Forα=−1,(26)R−1Δ=5.2429.


## 3.2.6. Ve-Degree-Based General Randić Index

Using Table4, we calculate ve-degree general Randić index:(27)RαveΔ=∑ℸℷ∈ΞΔδℸ+δℷα=23+4α+3+5α+23+7α+4+6α+24+7α+65+5α+25+6α+45+7α+26+7α+47+7α.Forα=1,(28)R1Δ=791.Forα=1/2,(29)R1/2Δ=141.0286.Forα=−1/2,(30)R−1/2Δ=4.9754.Forα=−1,(31)R−1Δ=0.9919.


## 3.2.7.D-Based Modified Zagreb Index

Using Table5, we calculate D-based modified Zagreb index(32)MmΔ=∑ℷ∈VΔ1δℷ2=7+1022+732+142=10.34.


## 3.2.8. Ev-D-Based Modified Zagreb Index

Using Table2, we calculate ev-degree modified Zagreb index:(33)MmevΔ=∑e∈ΞΔ1δeve2=8×142+13×152+3×162+172=1.1237.


## 3.2.9. Ve-Degree-Based Modified Zagreb Index

Using Table4, we calculate ve-degree modified Zagreb index(34)MmveΔ=∑ℷ∈VΔ1δveℷ2=532+242+852+162+172+142+152+162+472+172=1.28.


## 3.2.10.D-Based F Index

Using Table5, we calculate D-based F index(35)FΔ=∑ℷ∈VΔδℷ3=7+1023+733+43=340.


## 3.2.11. Ev-D-Based F Index

Using Table2, we calculate ev-degree F index(36)F1evΔ=∑e∈ΞΔδeve3=8×43+13×53+3×63+73=3128.


## 3.2.12. Ve-Degree-BasedF Index

Using Table6, we calculate ve-degree F index(37)F1veΔ=∑ℷ∈VΔδveℷ3=533+243+853+63+73+43+53+63+473+73=3942.In Figure3, all the derived indices are shown in the graphical ways. The different behaviors of the indices can be seen in the figure. In table 3 results of these TIs are given.Figure 3
Graphical analysis of the topological indices.


## 4. Conclusion

Topological descriptors have an important role in the study of QSPR/QSAR and predict the properties of chemical compounds. Fenofibrate is a drug that is used in conjunction with a healthy diet to lower cholesterol and triglyceride (fat-like substance) levels in the blood. This could help prevent pancreatitis (inflammation or swelling of the pancreas) caused by excessive triglyceride levels in the blood. In this study, we computeD-based first Zagreb index, ve-degree Zagreb α index, Zagreb β index, ev-degree Zagreb index, Randić index, ve-degree Randić index, ev-degree Randić index, modified Zagreb index, ve-degree modified Zagreb index, ev-degree modified Zagreb index, F index, ve-degree F index, and ev-degree F index for fenofibrate. With the help of these, we can study the physicochemical properties of the fenofibrate. Chemical compound testing in a lab is very expensive and time-consuming, whereas TIs are simple to obtain. The production of the drug fenofibrate can be obtained in very low cost, which can be frequently used everywhere. Future work may be done to investigate TI for other drugs.



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*Source: 4477808-2022-08-21.xml*