Photonic crystals in biology

Poster Session, Tuesday, June 15
THE RANDIC INDEX OF DENDRIMER NANOSTARS
A. Madanshekaf and M. Ghaneei
Dept. of Mathematics, Faculty of Sciences,
Semnan University, Semnan, Iran
Theme A1 - B702
Abstract
Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical
application, Randic index is one of them. The dendrimer nanostars is a synthesized molecule built up from branched unit called monomers. In
this article, we compute the Randic index of two types of polymer dendrimers and fullerene and G3 dendrimers. 1-3
Keywords: Randic index, dendrimer nanostars.
1. Introduction
denotes the degree of the vertex i. Randic introduce the
Randic index as
, where i-j ranging
over all pairs of adjacent vertices of G. This index has been
successfully correlated with physico-chemical properties of
organic molecules. Indeed if G is the molecular graph of a
saturated hydrocarbon then there is a strong correlation
to all properties of dendrimers nanostars, but general
topological indices are considered in our present work.
Figure 2. Fullerene dendrimer
2. Results and discussion
denote the number of edges of G connecting vertices of
. 12-13
The aim of this section is to compute the Randic
index of these dendrimer nanostars.
Theorem 1. The Randic index of polymer
References
Figure 3. G 3 dendrimer
[1] Jevpraesesphant, R. et al., "The influence of surface
modification on the cytotoxicity of PAMAM
dendrimers", Int. J. Pharm., 252, 263266, 2003.
[2] Rissing, C.; Son, D. Y. "The Thiol-ene Reaction for the
Synthesis of Multifunctional Branched Organosilanes",
Organometallics 2008, 27, 5394-5397.
[3] "The application of the Diels-Alder reaction to polymer
syntheses based on furan / maleimide reversible couplings".
Polymeros vol. 15 no. 2 slo carlos April / June 2005.
Theorem 2. The Randic index of
dendrimer is computed as follows:
fullerene
6th Nanoscience and Nanotechnology Conference, İzmir, 2010 416-1