Geodesic
On planes trees with a~prescribed number of valency set realizations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 9-17.

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We describe valency sets of plane bicolored trees with a prescribed number of realizations by plane trees. Three special types of plane trees are defined: chains, trees of diameter 4, and special trees of diameter 6. We prove that there is a finite number of valency sets that have $R$ realizations as plane trees and do not belong to these special types. The number of edges of such trees is less than or equal to $12R+2$. The complete lists of valency sets of plane bicolored trees with 1, 2, or 3 realizations are presented. 
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N. M. Adrianov. On planes trees with a~prescribed number of valency set realizations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 9-17. http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a1/

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