Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
distance in a graph; interval function
distance in a graph; interval function
Summary:
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.
References:
[1] H.-J. Bandelt and V. Chepoi: A Helly theorem in weakly modular space. Discrete Math. 160 (1996), 25–39. DOI 10.1016/0012-365X(95)00217-K | MR 1417558
[2] H.-J. Bandelt, M. van de Vel and E. Verheul: Modular interval spaces. Math. Nachr. 163 (1993), 177–201. DOI 10.1002/mana.19931630117 | MR 1235066
[3] H. M. Mulder: The Interval Function of a Graph. Mathematish Centrum, Amsterdam, 1980. MR 0605838 | Zbl 0446.05039
[4] H. M. Mulder: Transit functions on graphs. In preparation. Zbl 1166.05019
[5] L. Nebeský: A characterization of the interval function of a connected graph. Czechoslovak Math. J. 44(119) (1994), 173–178. MR 1257943
[6] L. Nebeský: Characterizing the interval function of a connected graph. Math. Bohem. 123 (1998), 137–144. MR 1673965
Search
Partner of
