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 - I I . 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 - I I .

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.

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

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 R1(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u) + rG(v)] and R2(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u)rG(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 HR1(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u) + rG(v)]2 and HR2(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u)rG(v)]2. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

Chemical graph theory plays an important role in modeling and designing any chemical structure. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. In this paper, we study the chemical graph of the crystal structure of titanium difluoride TiF 2 and the crystallographic structure of cuprite Cu 2 O. Furthermore, we compute degree-based topological indices, mainly ABC, GA, ABC 4 , GA 5 and general Randić indices. Furthermore, we also give exact results of these indices for the crystal structure of titanium difluoride TiF 2 and the crystallographic structure of cuprite Cu 2 O.