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 are numbers related to sub-atomic graphs to allow quantitative structure-movement/property/danger connections. These topological indices correspond to some specific physico-concoction properties such as breaking point, security, strain vitality of chemical compounds. The idea of topological indices were set up in compound graph hypothesis in view of vertex degrees. These indices are valuable in the investigation of mitigating exercises of specific Nanotubes and compound systems. In this paper, we discuss Zagreb types of indices and Zagreb polynomials for a few Nanotubes covered by cycles.

Background:: “Cerium oxide nanoparticles ( Aim and Objective:: The study“was aimed to analyze the chemical graph of crystal structure of Ceria Oxide(cuprite) Materials and Methods:: Chemical“graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. For calculation, we have utilized the combinatorial processing strategy, edge partition technique, vertex partition strategy, analytic procedures, graph hypothetical tools, degree counting technique and entirety of degrees of neighbors technique. Moreover, Matlab programming have been utilized for the numerical computations and checks. We likewise utilized the maple for plotting these numerical outcomes.” Results:: We have“computed Heat of Formation and Entropy using degree based topological indices. More oreciously, our main results are based on some degree based topological indices, namely, the atom bond connectivity index Conclusion:: We discuss“these indices exhibited difference with the reported heat of formation and entropy of cuprite

A nanostructure belong to a significant and an extensively investigated compounds in chemical science. It has been derived through engineering mechanism at the molecular scale. The most important of these new materials are carbon nanotubes. Carbon nanosheets are 2-dimensional lattices of carbon nanotubes. To compute and study topological indices of nanostructures are a respected problem in nanotechnology. Quantitative structure-property and structure-activity relationships of the carbon nanotubes compounds necessitate expressions for the molecular topological features of these compounds. Topological indices are vital devices for investigating chemical compounds to comprehend the fundamental topology of chemical structures. Ev-degree and ve-degree based topological indices are two novel degrees based indices as of late defined in chemical graph theory. In this paper, we have computed topological indices based on ev-degree and ve-degree for the two significant classes of carbon nanosheets composed by C₄ and C₈ denoted by $T^1{C}_4{C}_8(S)[p,q]$ and $T^2{C}_4{C}_8(R)[p,q].$

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to molecular structure of a chemical compounds then it reflects the theoretical properties of the chemical compounds. In this article, well-known degree based topological indices are applied on chemical structures of medicine used for treatment of breast cancer. Chemical structure is considered as graph, where elements are taken as vertices and bounds between them are taken as edges. Further, QSPR analysis of said topological indices are discussed and it is shown that these topological indices are highly correlated with the physical properties of chemical compounds used for the treatment of breast cancer.