𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Metric transforms of finite spaces and connected graphs

✍ Scribed by Hiroshi Maehara

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
723 KB
Volume
61
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

A metric transform of a semimetric space X is obtained from X by measuring the distances by a different (not always proportional) scale. Two semimetric spaces are said to be isomorphic if one is isometric to a metric transform of the other. If X is a finite semimetric space, then it will be shown that X is isomorphic to a subset of a euclidean space. The dimension of X is defined to be the minimum dimension of a euclidean space containing an isomorph of X. In this paper we examine scales and dimensions for finite semiraetric spaces, especially, for connected graphs and trees as metric spaces. We also count the number of non-isomorphic semimetric spaces.

πŸ“œ SIMILAR VOLUMES

Cartesian Products of Graphs and Metric
Cartesian Products of Graphs and Metric Spaces
✍ S. Avgustinovich; D. Fon-Der-Flaass πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 68 KB

We prove uniqueness of decomposition of a finite metric space into a product of metric spaces for a wide class of product operations. In particular, this gives the positive answer to the long-standing question of S. Ulam: 'If U Γ— U V Γ— V with U , V compact metric spaces, will then U and V be isometr

Centroids and medians of finite metric s
Centroids and medians of finite metric spaces
✍ Hans- JÜRgen Bandelt πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 709 KB

## Abstract The median of a weighted finite metric space consists of the points minimizing the total weighted distance to the points of the space. The centroid is formed by the points __p__ satisfying the following minimax condition: the maximal weight of a geodesically convex set not containing a