%0 Journal Article
%T Labelled and unlabelled enumeration of $k$-gonal 2-trees
%A G. Labelle
%A C. Lamathe
%A P. Leroux
%J Mathematics
%D 2003
%I arXiv
%X In this paper, we generalize 2-trees by replacing triangles by quadrilaterals, pentagons or $k$-sided polygons ($k$-gons), where $k\geq 3$ is fixed. This generalization, to $k$-gonal 2-trees, is natural and is closely related, in the planar case, to some specializations of the cell-growth problem. Our goal is the labelled and unlabelled enumeration of $k$-gonal 2-trees according to the number $n$ of $k$-gons. We give explicit formulas in the labelled case, and, in the unlabelled case, recursive and asymptotic formulas.
%U http://arxiv.org/abs/math/0312424v1