Geodesic
On the Enumeration of Tree-Rooted Maps
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 174-183

Voir la notice de l'article provenant de la source Cambridge University Press

It is the purpose of this paper to show that many of the enumerative techniques available for counting rooted plane trees may be extended to tree-rooted maps, that is, rooted maps in which a spanning tree is distinguished as root tree. For example, tree-rooted maps are enumerated by partition, and the average number of trees in a rooted map with n edges is determined. An enumerative similarity between Hamiltonian rooted maps (that is, rooted maps with a distinguished Hamiltonian polygon) and tree-rooted maps is discussed. A 1-1 correspondence is established between treerooted maps with n edges and Hamiltonian rooted trivalent maps with 2n + 1 vertices in which the root vertex is exceptional, being divalent, both of which are in 1-1 correspondence with non-separable Hamiltonian-rooted triangularized digons with n internal vertices, where both the latter are as defined in (2). 
Mullin, R. C. On the Enumeration of Tree-Rooted Maps. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 174-183. doi: 10.4153/CJM-1967-010-x
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