The distance matrix of a graph and its tree realization-Reference-Cited by-同舟云学术

The distance matrix of a graph and its tree realization

Published:1972 Issue:3 Volume:30 Page:255-269
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Patrinos A. N.,Hakimi S. L.

Abstract

The results of Hakimi and Yau and others in the realization of a distance matrix are generalized to graphs (digraphs) whose branches (arcs) may have negative weights. Conditions under which such matrices have a tree, hypertree or directed tree realization are given, uniqueness of these realizations is discussed and algorithms for their construction are indicated.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1972-30-03/S0033-569X-1972-0414405-8/S0033-569X-1972-0414405-8.pdf

Reference12 articles.

1. R. W. Floyd, Algorithm 97: shortest path, Comm. ACM 5, 345 (1962)

2. Distance matrix of a graph and its realizability;Hakimi, S. L.;Quart. Appl. Math.,1965

3. Realizing the distance matrix of a graph;Goldman, A. J.;J. Res. Nat. Bur. Standards Sect. B,1966

4. Constructing a tree on the basis of a set of distances between the hanging vertices;Zareckiĭ, K. A.;Uspehi Mat. Nauk,1965

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