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Treelike Families of Multiweights

Author

Listed:
  • Agnese Baldisserri

    (Dipartimento di Matematica e Informatica “U. Dini”)

  • Elena Rubei

    (Dipartimento di Matematica e Informatica “U. Dini”)

Abstract

Let T = (T,w) be a weighted finite tree with leaves 1, ..., n. For any I := {i1, ..., ik} ⊂ {1, ..., n}, let DI (T ) be the weight of the minimal subtree of T connecting i1, ..., ik; the DI (T ) are called k-weights of T . Given a family of real numbers parametrized by the k-subsets of 1 … n , D I I ∈ 1 … n k , $$ \left\{1,\dots, n\right\},{\left\{{D}_I\right\}}_{I\in \left(\underset{k}{\left\{1,\dots, n\right\}}\right)}, $$ we say that a weighted tree T = (T,w) with leaves 1, ..., n realizes the family if DI (T ) = DI for any I. Weighted graphs have applications in several disciplines, such as biology, archaeology, engineering, computer science, in fact, they can represent hydraulic webs, railway webs, computer networks...; moreover, in biology, weighted trees are used to represent the evolution of the species. In this paper we give a characterization of the families of real numbers parametrized by the k-subsets of some set that are realized by some weighted tree.

Suggested Citation

  • Agnese Baldisserri & Elena Rubei, 2018. "Treelike Families of Multiweights," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 367-390, July.
    • Handle: RePEc:spr:jclass:v:35:y:2018:i:2:d:10.1007_s00357-018-9260-3
    DOI: 10.1007/s00357-018-9260-3
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    References listed on IDEAS

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    1. Sven Herrmann & Katharina Huber & Vincent Moulton & Andreas Spillner, 2012. "Recognizing Treelike k-Dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 321-340, October.
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    Cited by:

    1. Simone Calamai, 2020. "Moduli Space of Families of Positive (n − 1)-Weights," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 317-327, July.

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    Keywords

    Weighted trees; Dissimilarity families;

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