Distance based indices in nanotubical graphs: part 2

Nanotubical graphs are obtained by wrapping a hexagonal grid, and then possibly closing the tube with caps. In this paper we show that the asymptotics for Balaban, Sum-Balaban, and Harary indices for all nanotubical graphs of type (k, l) on n vertices are 9 pi(k+ l)/2n, 9 root 2/2 root k + l. log(1+ root 2) and (k+ l) n log (n), respectively. In all the cases, the leading term depends on the circumference of the nanotubical graph, but not on its specific type. Thus, we conclude that these distance based topological indices seem not to be the most suitable for distinguishing nanotubes with the same circumference as far as the leading term is concerned.