Geodesic
An optimal problem in graph theory
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 355-359.

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The following problem is solved: determine a point on a tree having the property that the sum of the products of the intensities of its vertices by the corresponding distances to that point is a minimum. The proposed algorithm is reduced to the stepwise application to the tree of truncation of its vertices. A feasible interpretation of the problem is given. 
@article{MZM_1971_10_3_a13,
     author = {M. A. Dukhovnyi},
     title = {An optimal problem in graph theory},
     journal = {Matemati\v{c}eskie zametki},
     pages = {355--359},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a13/}
}
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M. A. Dukhovnyi. An optimal problem in graph theory. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 355-359. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a13/