Geodesic
Statuses and branch-weights of weighted trees
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1019-1025.

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In this paper we show that in a tree with vertex weights the vertices with the second smallest status and those with the second smallest branch-weight are the same.
Classification : 05C05, 05C12
Keywords: tree; status; branch-weight; median; centroid; second median; second centroid 
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     author = {Lin, Chiang and Shang, Jen-Ling},
     title = {Statuses and branch-weights of weighted trees},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1019--1025},
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     volume = {59},
     number = {4},
     year = {2009},
     mrnumber = {2563574},
     zbl = {1224.05148},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a11/}
}
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Lin, Chiang; Shang, Jen-Ling. Statuses and branch-weights of weighted trees. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1019-1025. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a11/