On topological indices of carbon nanocones and nanotori

Abstract

Let G be a graph with n vertices and d i is the degree of its ith vertex (d i is the degree of v i ). In this article, we compute the redefined first Zagreb index, redefined second Zagreb index, redefined third Zagreb index, augmented Zagreb index of graphs carbon nanocones CNC k [n], and nanotori [C 4 C 6 C 8 (p,q)]. Also, compute the multiplicative redefined first Zagreb index, multiplicative redefined second Zagreb index, multiplicative redefined third Zagreb index, multiplicative augmented Zagreb index of carbon nanocones CNC k [n], and nanotori [C 4 C 6 C 8 (p,q)]. K E Y W O R D Saugmented Zagreb index, carbon nanocones, nanotori, re-defined Zagreb index, topological index 1 | INTRODUCTION Mathematical chemistry is a branch of theoretical chemistry that investigate the molecular structure using graph theory. In other words, by specifies the vertices, edges, and degree vertices graph of the molecular structure, it certain the properties of the chemistry of this structure using mathematical methods. These methods solve many of the problems of chemistry. The theory of chemical graphs is a branch of mathematical chemistry, in fact, graph theory is connectivity between chemistry and mathematics, and solves many of the difficult problems of mathematical chemistry using graph theory, for more details you can see References [1-3] The topologic index is known as a connection index, in fact, the topology index describes the chemical composition based on the molecular structure. [4][5][6] Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. [7] Writing the mathematical model of a problem in various science is a helpful tool which helps a great deal to their progress. As an example, a graph can be drawn in chemistry based on atoms and the existing bonds between them for every molecule and the graph mathematical models can be defined in order to analyze the molecule. Topological indices are one of the mathematical models that can be defined by assigning a real number to the chemical molecule.Topological indices of large chemical structures such as metal organic frameworks can be extremely useful in both characterization of structures and computing their physicochemical properties that are otherwise difficult to compute for such large networks of importance in reticular chemistry. Synthesis of novel reticular metal-organic frameworks and networks in which covalent fibers are weaved into crystals are becoming increasingly important in recent years. [8,9] Topological indices numerically represent the structural characteristics of molecules that are obtained by the use of graph-theoretical concepts applied to these large networks of interest in reticular chemistry. In addition, the mathematical techniques comprising of group theory a...

[Retracted] On the Temperature Indices of Molecular Structures of Some Networks

“…In [6], the authors obtained some of the new results for anticancer drugs by using the multiplicative topological indices. In [12], the author discussed carbon nanocones and nanotori by using some of the topological indices. erefore, in this paper, we obtain new results for OTIS networks by using some topological indices.…”

Structural investigation of carbon nanocone through topological coindices

“…Graph theory is applied broadly in the field of nanotechnology, specifically in nanostructures, in which carbon has been the central attention in the intense research activity [6][7][8]. Ge and Sattler discovered carbon nanocones (CNCs) in the year 1994 [9].…”

On topological indices and entropies of diamond structure

“…Prior studies, such as those by Hui et al [15] and Jahanbani [16], have demonstrated the significance of using topological descriptors and entropies to predict physical properties. These studies employed the quantitative structure‐property relationship (QSPR) methodology, a widely recognized analytical approach for numerically characterizing molecular features.…”