Geodesic
On the number of labeled $k$-arch graphs
Journal of integer sequences, Tome 10 (2007) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we deal with $k$-arch graphs, a superclass of trees and $k$-trees. We give a recursive function counting the number of labeled $k$-arch graphs. Our result relies on a generalization of the well-known Prüfer code for labeled trees. In order to guarantee the generalized code to be a bijection, we characterize the valid code strings.
Classification : 05A15, 05C30, 05A10
Keywords: k-arch graphs, trees, k-trees, coding, pr$\ddot $ufer code, Cayley's formula 
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     author = {Caminiti, Saverio and Fusco, Emanuele G.},
     title = {On the number of labeled $k$-arch graphs},
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     number = {7},
     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a5/}
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Caminiti, Saverio; Fusco, Emanuele G. On the number of labeled $k$-arch graphs. Journal of integer sequences, Tome 10 (2007) no. 7. http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a5/