Some new degree based topological indices of hnaphtalenic graph via M-polynomial approach (original) (raw)

COMPUTING SOME TOPOLOGICAL INDICES OF CARBON NANOTUBES

In this paper, several topological indices are investigated for H-Phenylenic nanotube, H-Naphthylenic nanotube and H-Anthracenic nanotube. The calculated indices are product-connectivity index, sum-connectivity index, geometric-arithmetic index and atom-bond connectivity index.

On certain degree-based topological indices of armchair polyhex nanotubes

2018

Recently [18], Shigehalli and Kanabur have introduced two new topological indices namely, AG2 index and SK3 index. Hosamani [14], has studied a novel topological index, namely the Sanskruti index S (G) of a molecular graph G. In this paper, formula for computing the armchair polyhex nanotube TUAC6 [m, n] family is given.

Computing Degree-Based Topological Indices of Polyhex Nanotubes

2016

Recently, Shigehalli and Kanabur [20] have put forward for new degree based topological indices, namely Arithmetic-Geometric index (AG1 index), SK index, SK1 index and SK2 index of a molecular graph G. In this paper, we obtain the explicit formulae of these indices for Polyhex Nanotube without the aid of a computer.

Derivation of mathematical closed form expressions for certain irregular topological indices of 2D nanotubes

Scientific Reports, 2023

A numeric quantity that characterizes the whole structure of a network is called a topological index. In the studies of QSAR and QSPR, the topological indices are utilized to predict the physical features related to the bioactivities and chemical reactivity in certain networks. Materials for 2D nanotubes have extraordinary chemical, mechanical, and physical capabilities. They are extremely thin nanomaterials with excellent chemical functionality and anisotropy. Since, 2D materials have the largest surface area and are the thinnest of all known materials, they are ideal for all applications that call for intense surface interactions on a small scale. In this paper, we derived closed formulae for some important neighborhood based irregular topological indices of the 2D nanotubes. Based on the obtained numerical values, a comparative analysis of these computed indices is also performed. Carbon nanotubes (CNTs) are actually cylindrical molecules that comprise of rolled-up sheets of single-layer carbon atoms (graphene). They can be single-walled having a less than 1 nm (nm) diameter or multi-walled, comprising of numerous concentrically interlinked nanotubes, with around more than 100 nm diameters. Sumio Iijima discovered the multi-walled carbon nanotubes in 1991 1. CNTs are bonded with sp 2 bonds chemically, an extremely strong form of molecular interaction. These nanotubes inherit electrical properties from graphene, which are determined by the rolling-up direction of the graphene layers. Apart from these, CNTs also have distinctive mechanical and thermal properties like lightweight , high tensile strength, low density, better thermal conductivity, high aspect ratio and high chemical stability. All these properties make them intriguing for new materials development, especially CNTs are best candidates for hydrogen storage cells, cathode ray tubes (CRTs), electronic devices, electron field emitters and transistors. Keeping in view their strong applicability and importance, it is very important to model and characterize these CNTs for a better understanding of their structural topology for enhancement of their physical properties. The study of chemicals using a mathematical method is called mathematical chemistry. Chemical graph theory is a branch of chemistry that uses graph theory concepts to convert chemical events into mathematical models. The chemical graph is a simple connected graph in which atoms and chemical bonds are taken as vertices and edges respectively. A connected graph of order n = |V (G)| and size m = |E(G)| can be created with the help of G and edge set E. The focus of research in the area of nanotechnology is on atoms and Molecules. The Cartesian product of a path graph of m and n is called a 2D lattice. Graph theory has emerged as a powerful tool for analyzing the structural properties of complex systems represented by graphs. Topological indices, which are numerical quantities derived from graph theory 2-8 , have gained significant attention due to their ability to concisely capture important graph properties. Degree-based topological indices specifically utilize the degrees of vertices in a graph to quantify its structural characteristics 9. Degree based indices, such as the Randić index, the atom-bond connectivity index, and the Harary index, capture the connectivity and branching patterns in a graph by considering the distances between pairs of vertices in relation to their degrees 10-14. These indices have found wide applications in drug design, chemical graph theory, and network analysis 15-18 .

On Edge Version of Some Degree-Based Topological Indices of HAC5C7 [p,q] and VC5C7[p,q] Nanotubes

Polycyclic Aromatic Compounds, 2020

A graph in which atoms are taken as vertices and bonds can be shown by edges is called a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties. Industry is flourishing nowadays just because of the interdisciplinary study of different subjects. This gives us a way to understand the application of different subjects. Chemical graph theory is a mixture of chemistry and mathematics both play an important role in chemical graph theory. Chemistry provides a chemical compound and graph theory transform this chemical compound into a molecular graph which further studied by different aspects such as topological indices. In this article, we computed generalized Randi c, general Zagreb, general sum-connectivity, ABC, GA, ABC 4 , and GA 5 indices of line graphs of the HAC 5 C 7 p, q ½ and VC 5 C 7 p, q ½ nanotubes."

Some Formulas for the Polynomials and Topological Indices of Nanostructures

Acta Chemica Iasi, 2016

In this paper, we focus on the structure of Polycyclic Aromatic Hydrocarbons (PAHs) and calculate the Omega and its related counting polynomials of nanostructures. Also, the exact expressions for the Theta, Sadhana, Pi, Hyper Zagreb and Forgotten Zagreb indices of linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori were computed for the first time. These indices can be used in QSAR/QSPR studies.

Computation of the different topological indices of nanostructures

In this research study, several topological indices have been investigated for linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori. The calculated indices are first, second, third and modified second Zagreb indices. In addition, the first and second Zagreb coindices of these nanostructures were calculated. The explicit formulae for connectivity indices of various families of Tetracenic nanotubes and nanotori are presented in this manuscript. These formulae correlate the chemical structure of nanostructures to the information about their physical features.