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

Mathematica Bohemica (2001)

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

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topNebeský, 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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- An algebraic characterization of geodetic graphs, Czechoslovak Math. J. 48 (1998), 701–710. (1998) MR1658245
- Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962. (1962) Zbl0105.35401MR0150753

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