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The application of graph theory in the study of molecular physical and chemical properties involves theoretical mathematical chemistry. Atoms, represented by vertices, and edges, represented by bonds between them, are detailed in simple graphs called chemical graphs. The mathematical derivation of the numerical value of a graph is called the molecular descriptor of the graph. Any connected graph wherein no edge is contained in exclusive of a single cycle is called a cactus graph. In the research in this article, expressions for various molecular descriptors of line graph of the graph obtained by the rooted product of the cycle and path graphs are constructed. This article obtained the calculation of molecular descriptors for line graphs of chain ortho cactus and chain para cactus graphs. To predict the biological activity of a compound, the generalized Zagreb index, the first Zagreb index  M 1 G , the second Zagreb index  M 2 G , the F-index, the general Randic index, the symmetric division, the atom bond connectivity (ABC), and the geometric arithmetic (GA) descriptors are created.

Molecular Descriptors on Line Graphs of Cactus Chains and Rooted Products Graphs