The interval function of a connected graph and a characterization of geodetic graphs

Ladislav Nebeský

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 247-254
  • ISSN: 0862-7959

Abstract

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The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize properties of the interval function.

How to cite

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Nebeský, Ladislav. "The interval function of a connected graph and a characterization of geodetic graphs." Mathematica Bohemica 126.1 (2001): 247-254. <http://eudml.org/doc/248837>.

@article{Nebeský2001,
abstract = {The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize properties of the interval function.},
author = {Nebeský, Ladislav},
journal = {Mathematica Bohemica},
keywords = {graphs; distance; interval function; geodetic graphs; distance; interval function; geodetic graphs},
language = {eng},
number = {1},
pages = {247-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The interval function of a connected graph and a characterization of geodetic graphs},
url = {http://eudml.org/doc/248837},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - The interval function of a connected graph and a characterization of geodetic graphs
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 247
EP - 254
AB - The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize properties of the interval function.
LA - eng
KW - graphs; distance; interval function; geodetic graphs; distance; interval function; geodetic graphs
UR - http://eudml.org/doc/248837
ER -

References

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  1. 10.1002/jgt.3190120410, J. Graph Theory 12 (1988), 533–549. (1988) MR0968750DOI10.1002/jgt.3190120410
  2. Three interval conditions for graphs, Ars Combin. 29B (1990), 213–223. (1990) MR1412877
  3. 10.1002/jgt.3190180705, J. Graph Theory 18 (1994), 681–703. (1994) MR1297190DOI10.1002/jgt.3190180705
  4. The Interval Function of a Graph, Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980. (1980) Zbl0446.05039MR0605838
  5. A characterization of the set of all shortest paths in a connected graph, Math. Bohem. 119 (1994), 15–20. (1994) MR1303548
  6. A characterization of the interval function of a connected graph, Czechoslovak Math. J. 44 (1994), 173–178. (1994) MR1257943
  7. A characterization of geodetic graphs, Czechoslovak Math. J. 45 (1995), 491–493. (1995) MR1344515
  8. Characterizing the interval function of a connected graph, Math. Bohem. 123 (1998), 137–144. (1998) MR1673965
  9. 10.1023/A:1022435605919, Czechoslovak Math. J. 48 (1998), 701–710. (1998) MR1658245DOI10.1023/A:1022435605919
  10. Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962. (1962) Zbl0105.35401MR0150753

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