Geodesic
Characterizing the interval function of a connected graph
Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 137-144

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.1998.126307
Classification : 05C12
Keywords: graphs; distance; interval function 
Nebeský, Ladislav. Characterizing the interval function of a connected graph. Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 137-144. doi: 10.21136/MB.1998.126307
@article{10_21136_MB_1998_126307,
     author = {Nebesk\'y, Ladislav},
     title = {Characterizing the interval function of a connected graph},
     journal = {Mathematica Bohemica},
     pages = {137--144},
     year = {1998},
     volume = {123},
     number = {2},
     doi = {10.21136/MB.1998.126307},
     mrnumber = {1673965},
     zbl = {0937.05036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126307/}
}
TY  - JOUR
AU  - Nebeský, Ladislav
TI  - Characterizing the interval function of a connected graph
JO  - Mathematica Bohemica
PY  - 1998
SP  - 137
EP  - 144
VL  - 123
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126307/
DO  - 10.21136/MB.1998.126307
LA  - en
ID  - 10_21136_MB_1998_126307
ER  - 
%0 Journal Article
%A Nebeský, Ladislav
%T Characterizing the interval function of a connected graph
%J Mathematica Bohemica
%D 1998
%P 137-144
%V 123
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126307/
%R 10.21136/MB.1998.126307
%G en
%F 10_21136_MB_1998_126307

[1] H.-J. Bandelt M. van de Vel E.Verheul: Modular interval spaces. Math. Nachr. 163 (1993), 177-201. | DOI | MR

[2] H.-J. Bandelt V. Chepoi: A Holly theorem in weakly modular space. Discrete Math. 160 (1996), 25-39. | DOI | MR

[3] G. Chartrand L. Lesniak: Graphs & Digraphs. (third edition). Chapman & Hall, London, 1996. | MR

[4] H. M. Mulder: The Interval Function of a Graph. Mathematisch Centrum, Amsterdam, 1980. | MR | Zbl

[5] L. Nebeský: A characterization of the interval function of a connected graph. Czechoslovak Math. J. 44 (119) (1994), 173-178. | MR

[6] L. Nebeský: Geodesics and steps in a connected graph. Czechoslovak Math. J. 47 (122) (1997), 149-161. | DOI | MR

[7] E. R. Verheul: Multimedians in metric and normed spaces. CWI TRACT 91, Amsterdam, 1993. | MR | Zbl

Cité par Sources :