Subdominant pseudoultrametric on graphs

Journal Article · Sat Aug 31 00:00:00 EDT 2013 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2013V204N08ABEH004333· OSTI ID:22317916

Dovgoshei, A A; Petrov, E A ^[1]

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1. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

• OSTI ID: 22317916
• Journal Information: Sbornik. Mathematics, Vol. 204, Issue 8; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BIBLIOGRAPHIES
DIAGRAMS
GRAPH THEORY
METRICS