On the distance function of a connected graph
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1101-1106 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

An axiomatic characterization of the distance function of a connected graph is given in this note. The triangle inequality is not contained in this characterization.
An axiomatic characterization of the distance function of a connected graph is given in this note. The triangle inequality is not contained in this characterization.
Classification : 05C12, 05C40
Keywords: connected graph; distance function
@article{CMJ_2008_58_4_a16,
     author = {Nebesk\'y, Ladislav},
     title = {On the distance function of a connected graph},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1101--1106},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471169},
     zbl = {1174.05039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a16/}
}
TY  - JOUR
AU  - Nebeský, Ladislav
TI  - On the distance function of a connected graph
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 1101
EP  - 1106
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a16/
LA  - en
ID  - CMJ_2008_58_4_a16
ER  - 
%0 Journal Article
%A Nebeský, Ladislav
%T On the distance function of a connected graph
%J Czechoslovak Mathematical Journal
%D 2008
%P 1101-1106
%V 58
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a16/
%G en
%F CMJ_2008_58_4_a16
Nebeský, Ladislav. On the distance function of a connected graph. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1101-1106. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a16/

[1] Kay, D. C., Chartrand, G.: A characterization of certain ptolemaic graphs. Canad. J. Math. 17 (1965), 342-346. | DOI | MR | Zbl

[2] Mulder, H. M.: The interval function of a graph. Math. Centre Tracts 132, Math. Centre, Amsterdam (1980). | MR | Zbl

[3] Nebeský, L.: A characterization of the set of all shortest paths in a connected graph. Math. Bohem. 119 (1994), 15-20. | MR

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

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

[6] Nebeský, L.: A characterization of the interval function of a (finite or infinite) connected graph. Czech. Math. J. 51 (2001), 635-642. | DOI | MR | Zbl