graphs; distance; interval function
As was shown in the book of Mulder , the interval function is an important tool for studying metric properties of connected graphs. An axiomatic characterization of the interval function of a connected graph was given by the present author in . (Using the terminology of Bandelt, van de Vel and Verheul  and Bandelt and Chepoi , we may say that  gave a necessary and sufficient condition for a finite geometric interval space to be graphic).
In the present paper, the result given in  is extended. The proof is based on new ideas.
 G. Chartrand L. Lesniak: Graphs & Digraphs
. (third edition). Chapman & Hall, London, 1996. MR 1408678
 L. Nebeský: A characterization of the interval function of a connected graph
. Czechoslovak Math. J. 44 (119) (1994), 173-178. MR 1257943