Abstract
A numeric quantity which characterizes the whole structure of a graph is called a topological index. The concept of Randi ć
(H) , atom-bond connectivity (ABC) and geometric-arithmetic (GA) topological indices were established in chemical
graph theory based on vertex degrees. Later on, other versions of ABC and GA indices were introduced and some of the
versions of these indices are recently designed. Dendrimers are recognized as one of the major commercially available
nanoscale building blocks, large and complex molecules with well defined chemical structure. The nanostar dendrimer is a
part of a new group of macroparticles that appear to be photon funnels just like artificial antennas. A k -polyomino system is
a finite 2 -connected plane graph such that each interior face (also called cell) is surrounded by a regular 4k -cycle of length
one. In this article, we compute ABC , GA, and Randić indices of two important families of nanostar dendrimers. We also
compute fourth version of atom-bond connectivity ( ) 4 ABC index and fifth version of geometric-arithmetic ( ) 5 GA index
for graphs of 1 and 2 -polyomino chains of 8 -cycles..
Keywords
Randić index, Atom-bond connectivity (ABC) index, Geometric-arithmetic (GA) index, 4 ABC index, 5 GA
index, Nanostar dendrimers, k -polyomino system.
Citation
MUHAMMAD IMRAN, SAKANDER HAYAT, MUHAMMAD KASHIF SHAFIQ, On topological indices of nanostar dendrimers and polyomino chains, Optoelectronics and Advanced Materials - Rapid Communications, 8, 9-10, September-October 2014, pp.948-954 (2014).
Submitted at: June 25, 2014
Accepted at: Sept. 11, 2014