A characterization of the interval function of a (finite or infinite) connected graph

Ladislav Nebeský

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 3, page 635-642
  • ISSN: 0011-4642

Abstract

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By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.

How to cite

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Nebeský, Ladislav. "A characterization of the interval function of a (finite or infinite) connected graph." Czechoslovak Mathematical Journal 51.3 (2001): 635-642. <http://eudml.org/doc/30660>.

@article{Nebeský2001,
abstract = {By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.},
author = {Nebeský, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {distance in a graph; interval function; distance in a graph; interval function},
language = {eng},
number = {3},
pages = {635-642},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A characterization of the interval function of a (finite or infinite) connected graph},
url = {http://eudml.org/doc/30660},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - A characterization of the interval function of a (finite or infinite) connected graph
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 635
EP - 642
AB - By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.
LA - eng
KW - distance in a graph; interval function; distance in a graph; interval function
UR - http://eudml.org/doc/30660
ER -

References

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  1. 10.1016/0012-365X(95)00217-K, Discrete Math. 160 (1996), 25–39. (1996) MR1417558DOI10.1016/0012-365X(95)00217-K
  2. 10.1002/mana.19931630117, Math. Nachr. 163 (1993), 177–201. (1993) MR1235066DOI10.1002/mana.19931630117
  3. The Interval Function of a Graph, Mathematish Centrum, Amsterdam, 1980. (1980) Zbl0446.05039MR0605838
  4. Transit functions on graphs, In preparation. Zbl1166.05019
  5. A characterization of the interval function of a connected graph, Czechoslovak Math. J. 44(119) (1994), 173–178. (1994) MR1257943
  6. Characterizing the interval function of a connected graph, Math. Bohem. 123 (1998), 137–144. (1998) MR1673965

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