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Croatica Chemica Acta, Vol. 81 No. 2, 2008.

Original scientific paper

Growth in [n]helicenes

Primož Lukšič ; IMFM, University of Ljubljana, Ljubljana, Slovenia
Tomaž Pisanski ; IMFM, University of Ljubljana, Ljubljana, Slovenia; University of Primorska, Koper, Slovenia

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Abstract

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.

Keywords

growth function; polyhex; helicene; benzenoid graph; fasciagraph; Wiener index

Hrčak ID:

28148

URI

https://hrcak.srce.hr/28148

Publication date:

30.6.2008.

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