PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers

The nanostar dendrimer is part of a new group of macromolecules that appear to be photon funnels just like artificial antennas. It also shows good resistant to photo bleaching. The nanostar dendrimer promises great applications but first the structure and the energy transfer mechanism must be understood. Experimental and theoretical insight is needed in order to understand the energy transfer mechanism. Methodology Some algebraic definitions used for the study are given. Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. In a chemical graph, vertices represent atoms and edges represent bonds. These graphs have been used for affinity diagrams showing a relationship between chemical substances. Numbers reflecting certain structural features of a molecule that are obtained from its chemical graph are usually called topological indices. The Wiener index, W, one of widely used descriptors of molecular topology, was introduced in 1947 by Wiener 1 as the half-sum of all topological distances in the hydrogendepleted graph representing the skeleton of the molecule. Here, we denote by d(u,v), the topological distance between vertices u and v of the graph G, which is the length of a minimum path between these vertices. We encourage the readers to consult two survey articles by Dobrynin and his co-authors 2,3 and references therein for background material and historical aspect of Wiener index. Diudea 4-10 was the first scientist who investigated the mathematical properties of nanostructures. He and his team studied several nanostructures by computing their topological indices and designed a package named TopoCluj 11 for computing topological indices of the molecular graphs of nanostructures.