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Graph theory has various applications in chemistry and molecular structure research, and its importance has been growing continuously. In molecular graphs, points represent the atoms, and lines represent the chemical bonds between atoms. This article is about to show the precise evaluation for topological descriptors based on the degree sum of the neighbors of end vertices for some molecular structures. We derive for Sanskruti index, Neighborhood inverse sum index, Neighborhood Harmonic index, Fifth N D e index, and Neighborhood second modified Zagreb index for two-dimensional lattice structure of certain Nanotube and Nanotorus. [ABSTRACT FROM AUTHOR]

The topological indices are important tools in the chemical graph theory to model different physico-chemical properties of molecules. The Sanskruti index for a graph G having vertex set V(G) and edges set E(G) is defined as S (G) = ∑ u v ∈ E (G) δ G (u) δ G (v) δ G (u) + δ G (v) - 2 3 , where δ G (u) represents the degree sum of nodes adjacent to u ∈ V (G) . In this report, we argue that the chemical applicability of the S -index in the paper (Hosamani in J Appl Math Comput 54:425–433, 2017) is investigated incorrectly. In addition to correcting the result, we perform a comprehensive investigation to uncover the chemical significance of S . Some interesting mathematical features of the index are also explored by deriving some tight bounds with identifying the extremal graphs. [ABSTRACT FROM AUTHOR]

Sierpinski networks constitute an extensively studied class of graphs of fractal nature applicable in topology, mathematics of Tower of Hanoi, computer science, and Chemical graph theory. Recently the properties of Sierpinski networks have been studied like physico-chemical properties, thermodynamic properties, chemical activity, biological activity, metric dimension and degree based topological indices. In this paper, we further extend the study of Sierpinski networks and computed Zagreb types molecular descriptors (molecular topological indices) and their variants. [ABSTRACT FROM AUTHOR]

Topological indices as a molecular descriptors are important tools in (QSAR)/(QSPR) studies. The graph entropies with topological indices inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of chemical graphs and complex networks. The graph entropy measures are playing an important role in a variety of problem areas including, discrete mathematics, biology, and chemistry. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices of different degree together with the number of edges between different degree vertices.In this paper, we study the chemical graph of crystal structure of titanium difluoride TiF2 and crystallographic structure of cuprite Cu2O. Also, we compute entropies of these structures by making a relation of degree based topological indices namely first redefined Zagreb index, second redefined Zagreb index, third redefined Zagreb index, fourth Atom Bond Connectivity index, fifth Geometric Arithmetic index, Sanskruti index with the help of information function.

The Sanskruti index of a graph G is defined as S(G)=∑uv∈E(G)sG(u)sG(v)sG(u)+sG(v)−23,$$\begin{align*}S(G)=\sum_{uv\in{}E(G)}{\left(\frac{s_G(u)s_G(v)}{s_G(u)+s_G(v)-2}\right)}^3, \end{align*}$$where sG(u) is the sum of the degrees of the neighbors of a vertex u in G. Let Pn, Cn, Sn and Sn + e be the path, cycle, star and star plus an edge of n vertices, respectively. The Sanskruti index of a molecular graph of a compounds can model the bioactivity of compounds, has a strong correlation with entropy of octane isomers and its prediction power is higher than many existing topological descriptors.

Sanskruti index of a graph G (V (G) , E (G)) with vertex-set V (G) and edge-set E (G) is S (G) = ∑ u v ∈ E (G) ( S u S v S u + S v − 2) 3 , where S u = ∑ v ∈ N G (u) d v . In this paper, the extremal graphs in the class of unicyclic graphs are characterized with respect to the Sanskruti index, where the considered class of unicyclic graphs contains five different large families of graphs. [ABSTRACT FROM AUTHOR]

There are numerous applications of graph theory in the field of structural chemistry. In this paper, we compute the Sanskruti index S(G) of the Line graph of Subdivision Graph of cyclic hexagonal-square chain and nanocones CNCK[n] respectively. [ABSTRACT FROM AUTHOR]

Topological indices as a molecular descriptors are important tools in (QSAR) / (QSPR) studies. The graph entropies with topological indices inspired by Shannon's entropy concept become the information-theoretic quantities for measuring the structural information of chemical graphs and complex networks. The graph entropy measures are playing an important role in a variety of problem areas including, discrete mathematics, biology, and chemistry. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices of different degree together with the number of edges between different degree vertices. In this paper, we study the chemical graph of crystal structure of titanium difluoride TiF 2 and crystallographic structure of cuprite Cu 2 O. Also, we compute entropies of these structures by making a relation of degree based topological indices namely first redefined Zagreb index, second redefined Zagreb index, third redefined Zagreb index, fourth Atom Bond Connectivity index, fifth Geometric Arithmetic index, Sanskruti index with the help of information function. [ABSTRACT FROM AUTHOR]

Derived graphs such as line, total, subdivision, r-subdivision, etc. graphs are used in making complex calculations easier. A topological index is a mathematical formula which gives some mathematical value which can be commented to get information on some property of the real life situation, a molecule, a network, etc. which is modelled by means of the graph under investigation. Recently Hosamani [7] put forward a novel topological index, namely the Sanskruti index of a molecular graph G. In this paper we compute the Sanskruti index of the line graph of tadpole, wheel and ladder graphs using the notion of subdivision. [ABSTRACT FROM AUTHOR]

Recently, Hosamani [8], has studied a novel topological index, namely the Sanskruti index S(G) of a molecular graph G. The Sanskruti index S(G) shows good correlation with entropy of octane isomers. In this paper we compute the Sanskruti index S(G) of NHPX[m, n] and TUC4[m, n] nanotubes. [ABSTRACT FROM AUTHOR]

A numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions. [ABSTRACT FROM AUTHOR]

Inspired by recent work of augmented Zagreb index (AZI) we propose here a new topological index, Sanskruti index $$\mathcal {S}(G)$$ of a molecular graph G. In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. The Sanskruti index $$\mathcal {S}(G)$$ shows good correlation with entropy of an octane isomers. In this paper we compute the Sanskruti index $$\mathcal {S}(G)$$ of line graphs of subdivison graphs of 2D-lattice, nanotube and nanotorus of $$\textit{TUC}_{4}C_{8}[p,q]$$ . [ABSTRACT FROM AUTHOR]

The topological index of a molecular structure correlate certain physicochemical properties such as boiling point and stability of that molecular structure. Recently several topological indices have been introduced and studies have shown their association with certain physical and chemical properties of other molecules. Specifically, Zagreb, Atom-bound connectivity (ABC) and Sanskruti indices have been correlated with extent of branching, enthalpy and entropy of some organic molecules. In this study we have calculated Zagreb, Atom-bound connectivity (ABC) and Sanskruti indices (S) for Copper (I) oxide and Copper (II) oxide CuO. Additionally, from the experimentally available data, we calculated entropy and enthalpy per unit cell for both the oxides and compared with Atom-bound connectivity and Sanskruti indices. It appears that these indices have very poor relation with these physical properties in both oxides of copper and they may need some modifications to show considerable compliance as reported in other organic molecules."