Geodesic
Minimal trees with a given vertex-search number
Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 52-60 
P. A. Golovach. Minimal trees with a given vertex-search number. Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 52-60. http://geodesic.mathdoc.fr/item/DM_1992_4_2_a5/
@article{DM_1992_4_2_a5,
     author = {P. A. Golovach},
     title = {Minimal trees with a~given vertex-search number},
     journal = {Diskretnaya Matematika},
     pages = {52--60},
     year = {1992},
     volume = {4},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_2_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Minimal trees with given vertex-search number (an invariant of graphs which arises in case of consideration of a search problem on a graph) are considered. Families of all such trees for a given vertex-search number have been constructed, and the problem of enumeration of the minimal trees has been solved, as well.