In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube,...

Novel Raman tags with various reporter molecules embedded in between gold nanostar (AuNS) and gold nanoshell are developed, showing significantly enhanced surface-enhanced Raman scattering intensity compared to gold nanoparticle-based composites. Immunoassay using these AuNS@tag@shell structures is highly specific with sensitivity down to 0.1 pg mL-1 , and is capable of multiplex detection, mak...

Gold nanostars provide high sensitivity for single nanoparticle label-free biosensing. The nanostars present multiple plasmon resonances of which the lower energy ones, corresponding to the nanostar tips and core-tip interactions, are the most sensitive to environmental changes. Streptavidin molecules are detected upon binding to individual, biotin-modified gold nanostars by spectral shifts in ...

let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

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...

Let G= V E be a simple connected graph. The distance between two vertices of G is defined to be the length of the shortest path between the two vertices. There are topological indices assigned to G and based on the distance function which are invariant under the action of the automorphism group of G. Some important indices assigned to G are the Wiener, Szeged, and PI index which we will find th...

let g be a molecular graph. the wiener index of g is defined as the summation of alldistances between vertices of g. in this paper, an exact formula for the wiener index of a newtype of nanostar dendrimer is given.

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like bo...

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 isa wiener-szeged-like index developed very recently. this topological index is defined as thesummation of all sums of nu(e) and nv(e), over all edges of connected graph g.

To overcome the current limit of tip-enhanced spectroscopy that is based on metallic nano-probes, we developed a new scanning probe with a metallic nanostar, a nanoparticle with sharp spikes. A Au nanoparticle of 5 nm was first attached to the end of a tip through DNA-DNA hybridization and mechanical pick-up. The nanoparticle was converted to a nanostar with a core diameter of ∼70 nm and spike ...