QSPR Analysis of Chemical Graph Theory

In this paper, we find the values of four important degree-based topological indices of molecular graph of alkane isomers. Further, we show that these parameters are highly correlated with physical properties of alkane isomers. . ©2019 All rights reserved.


Introduction
Let G = (V, E) be a graph with n vertices and m edges. The degree of a vertex u V (G) is denoted by d G (u) and is the number of vertices that are adjacent to u. The edge connecting the vertices u and v is denoted by uv [4].
Chemical graph theory is the branch of mathematical chemistry. It is concerned with handling chemical graphs that represent chemical system. Hence chemical graph theory deals with analysis of all consequences of connectivity in a chemical system. It has found to be a useful tool in QSAR (Quantitative Structure-Activity Relationship) and QSPR (Quantitative Structure-Property Relationship) [8,5,14]. Numerous studies have been made relating to the above mentioned fields by using what are called topological indices. In 1975, Randic [10] proposed a topological index that has become one of the most widely used in both QSAR and QSPR studies.
Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena [4,2,11]. This theory had an important effect on the development of the chemical sciences.
, where d G (u) and d G (v) are the degrees of the vertices u and v in G.
are the degrees of the vertices u and v in G.

Motivation
By looking at the earlier results QSPR Analysis of Certain Degree-Based Topological Indices and QSPR Analysis of Degree-Based Topological Indices with physical properties of Benzenoid Hydrocarbons [7,5,6,13].

Data Sources and Analytical Method
Energy of Alkane isomers are taken from [19,7,12,5]. Seven physicochemical properties of Alkane isomers have been selected on the availability of a suitable body of data: boiling point (BP), critical temperature (CT ), critical pressure (CP), Molar volume (CV), Molar refraction (MR), Heat of Vaporization (HV), Surface tension (ST ). The values are compiled in Table 2.

Results and Discussion
In Table 3, the correlation coefficient of topological indices with physicochemical properties of alkane isomers are found to be good.

Regression Models
We have tested the following linear regression model where, P=Physical property, TI=Topological Index. Using (4.1), we have obtained the following different linear models for each degree-based topological index, which are listed below.    By inspection of the data in Table 4 to Table 7, it is possible to draw a number of conclusions for the given topological indices like invariants.
The QSPR study of AG 1 (G) index reveals that can be useful in predicting the boiling point, critical temperature, critical pressure, Molar volume, Surface tension, Heat of Vaporisation, Molar refraction of alkane isomers also from Table 4, one can easily verify that AG 1 (G) index shows good correlation with all physical properties of alkane isomers. We can see that the correlation coefficient value of AG 1 (G) index with physical properties of alkane isomers lies between -0.8514 to 0.9467.
Further, the correlation coefficient value of AG 1 (G) index is very high for the MR of alkane isomers with r =0.9467.Thus the QSPR study reveals that the AG 1 (G) index is an useful tool in predicting the     Table 5, one can easily verify that SK (G) index index shows good correlation with all physical properties of alkane isomers. We can see that the corre-lation coefficient value of SK (G) index with physical properties of alkane isomers lies between -0.7661 to 0.927. Further, the correlation coefficient value of SK (G) index index is very high for the MR of alkane isomers with r =0.927.Thus the QSPR study reveals that the SK (G) index index is an useful tool in predicting the physical properties of alkane isomers.
The QSPR study of SK 1 (G) index reveals that can be useful in predicting the boiling point, critical temperature, critical pressure, Molar volume, Surface tension, Heat of Vaporisation, Molar refraction of alkane isomers also from Table 6, one can easily verify that SK 1 (G) index shows good correlation with all physical properties of alkane isomers. We can see that the correlation coefficient value of SK 1 (G) index with physical properties of alkane isomers lies between -0.673 to 0.8959. Further, the correlation coefficient value of SK 1 index is very high for the CT of alkane isomers with r =0.8959.Thus the QSPR study reveals that the SK 1 (G) index is an useful tool in predicting the physical properties of alkane isomers.