Analysis of tagged sequences by line distance matrices and grid paths
The generating function of the sequence that represents the number of graph vertices at a given distance from the root is called the spherical growth function of the rooted graph. This mathematical notion is first applied to finite and infinite graphs representing _n_helicenes, the simplest nonplanar unbranched catacondensed benzenoid hydrocarbons. The calculation of growth function is then generalized to graphs that have an arbitrary connected graph in place of each hexagon and therefore represent a subclass of fasciagraphs. Also, the connection between the growth function of a finite graph and its Wiener index is established.