Graph theory is used for modeling, designing, analysis and understanding chemical structures or chemical networks and their properties. The molecular graph is a graph consisting of atoms called vertices and the chemical bond between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree based additive topological indices, namely hyper-Zagreb index, first multiple and second multiple Zagreb indices, and first and second Zagreb polynomials.

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone’s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In this paper, we focus on the molecular graph of (2D) silicon-carbon $S{i}_2{C}_3$ -I and $S{i}_2{C}_3$ - $II$ . Moreover, we have computed topological indices, namely general Randić Zagreb types indices, geometric arithmetic index, atom–bond connectivity index, fourth atom–bond connectivity and fifth geometric arithmetic index of $S{i}_2{C}_3$ -I and $S{i}_2{C}_3$ - $II$ .

Graph theory plays a vital role in modeling and designing any chemical structure or chemical network. Chemical graph theory helps in understanding the molecular structural properties of a molecular graph. The molecular graph consists of atoms called vertices and chemical bonds between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree-based additive topological indices, mainly the first and second Zagreb indexes, general Randić index, atom bond connectivity index, geometric arithmetic index, fourth atom bond connectivity index, and fifth geometric arithmetic index of carbon graphite denoted by CG(m, n) for t levels, and crystal structure cubic carbon denoted for n levels.

Let G be a connected graph with vertex set V ( G ) and edge set E ( G ). Recently, the Revan vertex degree concept is defined in Chemical Graph Theory. The first and second Revan indices of G are defined as R ₁ ( G ) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [ r _G ( u ) + r _G ( v )] and R ₂ ( G ) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [ r _G ( u ) r _G ( v )], where uv means that the vertex u and edge v are adjacent in G . The first and second hyper-Revan indices of G are defined as HR ₁ ( G ) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [ r _G ( u ) + r _G ( v )] ² and HR ₂ ( G ) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [ r _G ( u ) r _G ( v )] ² . In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of 2- $D$ silicon–carbon Si ₂ C ₃ - $I$ and Si ₂ C ₃ - $II$ and analyzed its topological properties. For this purpose, we have computed topological indices, namely forgotten topological index, augmented Zagreb index, and Balaban index, and redefined first, second, and third Zagreb indices of 2- $D$ silicon–carbon Si ₂ C ₃ - $I$ and Si ₂ C ₃ - $II$ .

The eccentricity ε _u of vertex u in a connected graph G , is the distance between u and a vertex farthermost from u . The aim of the present paper is to introduce new eccentricity based index and eccentricity based polynomial, namely modified augmented eccentric connectivity index and modified augmented eccentric connectivity polynomial respectively. As an application we compute these new indices for octagonal grid O n m $\begin{array}{} \displaystyle O_n^m \end{array}$ and we compare the results obtained with the ones obtained by other indices like Ediz eccentric connectivity index, modified eccentric connectivity index and modified eccentric connectivity polynomial ECP ( G , x ).