Distance-Based Indices for Some Families of Dendrimer Nanostars.

In theoretical chemistry, chemical compounds and drugs are modeled as graphs in which each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. Such a graph constructed according to a chemical compounds is often called its molecular graph and the indices defined over this molecular graph have been shown to be strongly correlated to various chemical properties of the compounds. In this paper, in terms of analyzing the structure of chemical molecular graph and the techniques of edge dividing, we report several distance-based indices for four families of dendrimer Nanostars, including second ABC index, second GA related indices, PI related indices and polynomials and Szeged related indices and polynomials. Furthermore, we discuss the distance-based indices of three kinds of widely appeared molecular structures: TC4C8 (R) Nanotorus, H-Naphtalenic nanotubes and 1,3-adamantane array. The formulations of second ABC index, second GA related indices, vertex PI and Szeged polynomials are manifested as additional conclusions. [ABSTRACT FROM AUTHOR]