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. Manoj Changat, Sandi Klavžar, Henry Martyn Mulder, The all-paths transit function of a graph
  2. Ladislav Nebeský, A characterization of the interval function of a (finite or infinite) connected 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, Extreme geodesic graphs
  7. Gary Chartrand, Ping Zhang, The forcing convexity number of a graph
  8. Ladislav Nebeský, The directed geodetic structure of a strong digraph
  9. Ladislav Nebeský, The induced paths in a connected graph and a ternary relation determined by them
  10. Ladislav Nebeský, The interval function of a connected graph and a characterization of geodetic graphs

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