Valency based topological indices of organosilicon dendrimers and cactus chains

Topological indices are the global parameters defined for the simple graphs such that they give the same numerical value if the graphs are isomorphic. These numbers are of much importance because of their chemical importance, they correlate certain physico-chemical properties of certain organic compounds such hydrocarbons etc. A chemical graph is a graph which is created from some molecular structure by applying some graphical operations. Valency is a local graph parameter, which is defined for every vertex as the number of connections with other vertices in a graph, just like for an atom in a molecule. Dendrimers are recognized as one of the major commercially available nanoscale building blocks, large and complex molecules with well defined chemical structure. Cactus chains are simple linear polymers which were first known as Husimi trees. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this article, we study general Randić, harmonic, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for organosilicon dendrimers and cactus chains of three types.