A topological index of graph 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 paper, well-known degree-based topological indices are applied on chemical structures of antituberculosis drugs. Chemical structure is considered as graph, where elements are taken as vertices and bounds between them are taken as edges. Furthermore, QSPR analysis of the said topological indices are discussed, and it is shown that these topological indices are highly correlated with the physical properties of antituberculosis drugs. This theocratical analysis may help the chemist and people working in pharmaceutical industry to predict properties of antituberculosis drugs without experimenting.

In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph $G=(V,E)$ , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.

In this article, we study the degree based molecular topological indices for some infinite families of Nanostar Dendrimers. We derive the analytical closed formulae for these classes of complex chemical networks. These results are very helpful in understanding and predicting the physico-chemical properties for these chemical structures (Nanostar dendrimers NS2[n], NS3[n], D2[n]).

A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph. Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, and geometric-arithmetic index GA are of great importance in the QSAR/QSPR analysis and are used to estimate the networks. In this area of research, graph theory has been found of considerable use. In this paper, the distinct degrees and degree sums of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. Utilizing these edge partitions, the closed formulae for some degree-based topological indices of the networks are deduced.