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.
Similar content being viewed by others
References
H.-J. Bandelt and V. Chepoi: A Helly theorem in weakly modular space. Discrete Math. 160 (1996), 25–39.
H.-J. Bandelt, M. van de Vel and E. Verheul: Modular interval spaces. Math. Nachr. 163 (1993), 177–201.
H. M. Mulder: The Interval Function of a Graph. Mathematish Centrum, Amsterdam, 1980.
H. M. Mulder: Transit functions on graphs. In preparation.
L. Nebeský: A characterization of the interval function of a connected graph. Czechoslovak Math. J. 44(119) (1994), 173–178.
L. Nebeský: Characterizing the interval function of a connected graph. Math. Bohem. 123 (1998), 137–144.
Rights and permissions
About this article
Cite this article
Nebesky, L. A Characterization of the Interval Function of a (Finite or Infinite) Connected Graph. Czechoslovak Mathematical Journal 51, 635–642 (2001). https://doi.org/10.1023/A:1013744324808
Issue Date:
DOI: https://doi.org/10.1023/A:1013744324808