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Enumeration of K-Trees and Applications
Mahendra Jani, Robert G. Rieper, and Melkamu Zeleke
Department of Mathematics, William Paterson University, Wayne, NJ 07470, USA
{janim, zelekem}@wpunj.edu
Annals of Combinatorics 6 (3) p.375-382 September, 2002
AMS Subject Classification: 05A15
Abstract:
A k-tree is constructed from a single distinguished k-cycle by repeatedly gluing other k-cycles to existing ones along an edge. If K is any nonempty subset of , then a K-tree is obtained as above using k-cycles with . In this paper, we enumerate ordered K trees, show that the ratio of terminal edges to total number of edges in k-trees is , and use the K-trees as models to enumerate planted plane cacti.
Keywords: K-trees, terminal edges, generating functions, generalized Catalan numbers, planted plane cacti

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