Chemical compounds and drugs are often modelled as graphs (for example, Polyhex Nanotubes and Dendrimer Nanostar) where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. The edge Wiener index of ...

Let G be a graph with vertex and edge sets V(G) and E(G), respectively. As usual, the distance between the vertices u and v of a connected graph G is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. Throughout the paper, a graph means undirected connected graph without loops and multiple edges. In chemical graph theory, a molecular gr...

The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{|U|}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some na...

General formulas are obtained for the vertex Padmakar-Ivan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a Wiener-Szeged-like index developed very recently. This topological index is defined as the summation of all sums of nu(e) and nv(e), over all edges of connected graph G.

Uniform PbS-Au nanostar-nanoparticle heterodimers consisting of one Au nanoparticle grown on one horn of a well-defined six-horn PbS nanostar were prepared using the PbS nanostars as growth substrates for the selective deposition of Au nanoparticles. The size of the Au nanoparticles on the horns of the PbS nanostars could be readily adjusted by changing the PbS concentration for the deposition ...

We performed cathodoluminescence (CL) spectroscopy and imaging in a high-resolution scanning electron microscope to locally and selectively excite and investigate the plasmonic properties of a multi-branched gold nanostar on a silicon substrate. This method allows us to map the local density of optical states from the nanostar with a spatial resolution down to a few nanometers. We resolve, both...

Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core [1,4]. These are key molecules in nanotechnology and can be put to good use. In this article, we compute the first geometricarithmetic index of two infinite classes of dendrimers.

Nanocatalysts that possess large amounts of atoms on sharp corners and edges and high indexed sites are known to be more catalytically active. We report here on a novel yet simple method to synthesize in large yields a very active platinum nanocatalyst; the multiarmed nanostar single crystal. We utilize a seed mediated method using tetrahedral nanoparticles that are also synthesized by a new an...