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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  2. Three interval conditions for graphs, Ars Combin. 29B (1990), 213–223. (1990) MR1412877
  3. Quasi-median graphs and algebras, J. Graph Theory 18 (1994), 681–703. (1994) MR1297190
  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. An algebraic characterization of geodetic graphs, Czechoslovak Math. J. 48 (1998), 701–710. (1998) MR1658245
  10. Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962. (1962) Zbl0105.35401MR0150753

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