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Title: Characterizing the interval function of a connected graph (English)
Author: Nebeský, Ladislav
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 123
Issue: 2
Year: 1998
Pages: 137-144
Summary lang: English
Category: math
Summary: As was shown in the book of Mulder [4], the interval function is an important tool for studying metric properties of connected graphs. An axiomatic characterization of the interval function of a connected graph was given by the present author in [5]. (Using the terminology of Bandelt, van de Vel and Verheul [1] and Bandelt and Chepoi [2], we may say that [5] gave a necessary and sufficient condition for a finite geometric interval space to be graphic). In the present paper, the result given in [5] is extended. The proof is based on new ideas. (English)
Keyword: graphs
Keyword: distance
Keyword: interval function
MSC: 05C12
idZBL: Zbl 0937.05036
idMR: MR1673965
DOI: 10.21136/MB.1998.126307
Date available: 2009-09-24T21:30:21Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] H.-J. Bandelt M. van de Vel E.Verheul: Modular interval spaces.Math. Nachr. 163 (1993), 177-201. MR 1235066, 10.1002/mana.19931630117
Reference: [2] H.-J. Bandelt V. Chepoi: A Holly theorem in weakly modular space.Discrete Math. 160 (1996), 25-39. MR 1417558, 10.1016/0012-365X(95)00217-K
Reference: [3] G. Chartrand L. Lesniak: Graphs & Digraphs.(third edition). Chapman & Hall, London, 1996. MR 1408678
Reference: [4] H. M. Mulder: The Interval Function of a Graph.Mathematisch Centrum, Amsterdam, 1980. Zbl 0446.05039, MR 0605838
Reference: [5] L. Nebeský: A characterization of the interval function of a connected graph.Czechoslovak Math. J. 44 (119) (1994), 173-178. MR 1257943
Reference: [6] L. Nebeský: Geodesics and steps in a connected graph.Czechoslovak Math. J. 47 (122) (1997), 149-161. MR 1435613, 10.1023/A:1022404624515
Reference: [7] E. R. Verheul: Multimedians in metric and normed spaces.CWI TRACT 91, Amsterdam, 1993. Zbl 0790.46008, MR 1244813


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