Characterizing the interval function of a connected graph

Ladislav Nebeský

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 2, page 137-144
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Nebeský, Ladislav. "Characterizing the interval function of a connected graph." Mathematica Bohemica 123.2 (1998): 137-144. <http://eudml.org/doc/248294>.

@article{Nebeský1998,
abstract = {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.},
author = {Nebeský, Ladislav},
journal = {Mathematica Bohemica},
keywords = {graphs; distance; interval function; graphs; distance; interval function},
language = {eng},
number = {2},
pages = {137-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizing the interval function of a connected graph},
url = {http://eudml.org/doc/248294},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - Characterizing the interval function of a connected graph
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 2
SP - 137
EP - 144
AB - 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.
LA - eng
KW - graphs; distance; interval function; graphs; distance; interval function
UR - http://eudml.org/doc/248294
ER -

References

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  1. H.-J. Bandelt M. van de Vel E.Verheul, 10.1002/mana.19931630117, Math. Nachr. 163 (1993), 177-201. (1993) MR1235066DOI10.1002/mana.19931630117
  2. H.-J. Bandelt V. Chepoi, 10.1016/0012-365X(95)00217-K, Discrete Math. 160 (1996), 25-39. (1996) MR1417558DOI10.1016/0012-365X(95)00217-K
  3. G. Chartrand L. Lesniak, Graphs & Digraphs, (third edition). Chapman & Hall, London, 1996. (1996) MR1408678
  4. H. M. Mulder, The Interval Function of a Graph, Mathematisch Centrum, Amsterdam, 1980. (1980) Zbl0446.05039MR0605838
  5. L. Nebeský, A characterization of the interval function of a connected graph, Czechoslovak Math. J. 44 (119) (1994), 173-178. (1994) MR1257943
  6. L. Nebeský, 10.1023/A:1022404624515, Czechoslovak Math. J. 47 (122) (1997), 149-161. (1997) MR1435613DOI10.1023/A:1022404624515
  7. E. R. Verheul, Multimedians in metric and normed spaces, CWI TRACT 91, Amsterdam, 1993. (1993) Zbl0790.46008MR1244813

Citations in EuDML Documents

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  1. Ladislav Nebeský, A characterization of the interval function of a (finite or infinite) connected graph
  2. Manoj Changat, Sandi Klavžar, Henry Martyn Mulder, The all-paths transit function of a graph
  3. Gary Chartrand, Ping Zhang, H -convex graphs
  4. Gary Chartrand, Ping Zhang, On graphs with a unique minimum hull set
  5. Gary Chartrand, Frank Harary, Ping Zhang, Geodetic sets in graphs
  6. Gary Chartrand, Ping Zhang, The forcing convexity number of a graph
  7. Gary Chartrand, Ping Zhang, Extreme geodesic graphs
  8. Ladislav Nebeský, The directed geodetic structure of a strong digraph
  9. Ladislav Nebeský, The interval function of a connected graph and a characterization of geodetic graphs
  10. Ladislav Nebeský, The induced paths in a connected graph and a ternary relation determined by them

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