Abstract
The Balaban and sum-Balaban indices of a connected graph G=(V,E) with m edges are
uv E D u D vmJ G( ) ( )11( )and
uv E D u D v
m
SJ G( ) ( )11
( )
, where is the cyclomatic number of G and D(v) is the summation of all distances
between a vertex v and all other vertices of G, respectively. In this paper, explicit formulas for the Balaban and sum-Balaban
indices index of the nanostar dendrimer NS[n] is derived according to a recursive relation of distances. Numerical values
show that the Balaban index of NS[n] is not more than two and is decreasing, and its sum-Balaban index is increasing on n..
Keywords
Distance, The Balaban index, The sum-Balaban index, Nanostar dendrimer.
Citation
RENFANG WU, ZIKAI TANG, HANYUAN DENG, The Balaban and sum-Balaban indices of the nanostar dendrimer NS[n], Optoelectronics and Advanced Materials - Rapid Communications, 7, 11-12, November-December 2013, pp.997-1001 (2013).
Submitted at: Nov. 21, 2012
Accepted at: Nov. 7, 2013