MATHEMATICA BOHEMICA, Vol. 123, No. 2, pp. 137-144 (1998)

Characterizing the interval function
of a connected graph

Ladislav Nebesky

Ladislav Nebesky, Filozoficka fakulta Univerzity Karlovy, nam. J. Palacha 2, 116 38 Praha 1, Czech Republic

Abstract: {As was shown in the book of Mulder [4], 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 [5]. (Using the terminology of Bandelt, van de Vel and Verheul [1] and Bandelt and Chepoi [2], we may say that [5] gave a necessary and sufficient condition for a finite geometric interval space to be graphic).
In the present paper, the result given in [5] is extended. The proof is based on new ideas}.

Keywords: graphs, distance, interval function

Classification (MSC2000): 05C12

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