Treelike Families of Multiweights

Agnese Baldisserri and Elena Rubei ()
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Agnese Baldisserri: Dipartimento di Matematica e Informatica “U. Dini”
Elena Rubei: Dipartimento di Matematica e Informatica “U. Dini”

Journal of Classification, 2018, vol. 35, issue 2, No 8, 367-390

Abstract: 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.

Keywords: Weighted trees; Dissimilarity families; 05C05; 05C12; 05C22 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00357-018-9260-3

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