Geodesic
Plane trees with nine edges. Catalog
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 159-195.

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Generalized Chebyshev polynomials and definition fields are computed for all pairwise nonisotopic plane trees with nine edges. 
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Yu. Yu. Kochetkov. Plane trees with nine edges. Catalog. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 159-195. http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a9/

[1] Bétréma J., Péré D., Zvonkin A., Plane Trees and Their Shabat Polynomials. Catalog, Technical Report LaBRI No 92-75, Bordeaux, 1992