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Article

Lin, Chiang ; Shang, Jen-Ling
Statuses and branch-weights of weighted trees. (English). Czechoslovak Mathematical Journal, vol. 59 (2009), issue 4, pp. 1019-1025
MSC: 05C05, 05C12 | MR 2563574 | Zbl 1224.05148
Keywords:
tree; status; branch-weight; median; centroid; second median; second centroid
Summary:
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.
References:
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[3] Kariv, O., Hakimi, S. L.: An algorithmic approach to network location problems. II: The $p$-medians, SIAM J. Appl. Math. 37 (1979), 539-560. DOI 10.1137/0137041 | MR 0549139 | Zbl 0432.90075
[4] Zelinka, B.: Medians and peripherians of trees. Arch. Math. (Brno) 4 (1968), 87-95. MR 0269541 | Zbl 0206.26105
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