Enumeration of K-Trees and Applications. Mahendra Jani, Robert G. Rieper, and Melkamu Zelekeâ. Department of Mathematics, William Paterson University, ...
c Birkh¨auser Verlag, Basel, 2002
Annals of Combinatorics 6 (2002) 375-382
Annals of Combinatorics
0218-0006/02/040375-8
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 Received November 9, 2001 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 {2, 3, 4, . . .}, then a K-tree is obtained as above using k-cycles with k ∈ K. In this paper, we enumerate ordered Ktrees, show that the ratio of terminal edges to total number of edges in k-trees is k−1 k , 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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