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The w-centroids and least w-central subtrees in weighted trees

Author

Listed:
  • Erfang Shan

    (Shanghai University
    Shanghai University)

  • Liying Kang

    (Shanghai University)

Abstract

Let T be a weighted tree with a positive number w(v) associated with each vertex v. A subtree S is a w-central subtree of the weighted tree T if it has the minimum eccentricity $$e_L(S)$$ e L ( S ) in median graph $$G_{LW}$$ G L W . A w-central subtree with the minimum vertex weight is called a least w-central subtree of the weighted tree T. In this paper we show that each least w-central subtree of a weighted tree either contains a vertex of the w-centroid or is adjacent to a vertex of the w-centroid. Also, we show that any two least w-central subtrees of a weighted tree either have a nonempty intersection or are adjacent.

Suggested Citation

  • Erfang Shan & Liying Kang, 2018. "The w-centroids and least w-central subtrees in weighted trees," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1118-1127, November.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:4:d:10.1007_s10878-017-0174-5
    DOI: 10.1007/s10878-017-0174-5
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    References listed on IDEAS

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    2. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
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