distance in a graph; interval function
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.
 H. M. Mulder: Transit functions on graphs
. In preparation. Zbl 1166.05019
 L. Nebeský: A characterization of the interval function of a connected graph
. Czechoslovak Math. J. 44(119) (1994), 173–178. MR 1257943
 L. Nebeský: Characterizing the interval function of a connected graph
. Math. Bohem. 123 (1998), 137–144. MR 1673965