Second Hyper-Zagreb Index of Titania Nanotubes and Their Applications

Abstract

Topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph, it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. In the other side, titania nanotube is a well-known semiconductor and has numerous technological applications such as biomedical devices, dye-sensitized solar cells, and etc. In this paper, the second Hyper-Zagreb index and their coindex of Titania nanotubes have been computed. Furthermore, strong correlation coefficients between second Hyper-Zagreb index and some physicochemical properties such as Density (DENS), Molar volume (MV), Acentric factor (Acenfac) and Entropy (S) have been Appeared.

An Analysis of Eccentricity‐Based Invariants for Biochemical Hypernetworks

“…We proposed a new approach to estimate the entropy by estimating its topological indices. e forgotten and the hyper Zagreb indices are employed to form the physico-chemical characteristics such as density, volume, entropy, and acentric factor of the underlying structure [35]. e degreebased entropy can also be employed to structural chemistry, social network, biology, ecological networks, and national security.…”

The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

“…Titania nanotubes are considered one of the most studied compounds in materials science. Owing to some outstanding properties, it is used, for instance, in photocatalysis, dye-sensitized solar cells, and biomedical devices [28], [29], [30]. In the following subsection, we study the second Hyper-Zagreb of molecular complement graph Titania nanotubes and molecular complement graph of nanotorus.…”

“…given in [28], [29]. HM2(T iO2[n, m]) = 1930mn+362n given in [30]. and the partitions of the vertex set and edge set V (T iO2), E(T iO2), of T iO2[n, m] nanotubes are given in (Tables 3, 4), respectively.…”

On Transformed Graphs

“…In [12], the study on the first hyper Zagreb index (HM 1 ) was initiated and certain results relevant to the mathematical techniques of graph operations were obtained. The study on another variant, the second hyper Zagreb index (HM 2 ), was initiated in [13] and computations pertaining to various classes graphs have been reported [14,15].…”