# Characterizing the interval function of a connected graph

Mathematica Bohemica (1998)

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

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topNebeský, 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

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

## Citations in EuDML Documents

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

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