On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

Abstract

Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively.
 HIGHLIGHTS
 
 Calculated degree based Topological indices of a 3D crystal from M-polynomial
 A relation among various Topological indices is established geometrically
 Variations of Topological Indices along three dimensions (directions) are shown geometrically
 Harmonic index approximates the degree variation of oxygen atom