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MATHEMATICA BOHEMICA, Vol. 126, No. 1, pp. 247-254 (2001)
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# The interval function of a connected graph and a characterization of geodetic graphs

## Ladislav Nebesky

* Ladislav Nebesky*, Univerzita Karlova v Praze, Filozoficka fakulta, nam. J. Palacha 2, 116 38 Praha 1, Czech Republic, e-mail: ` ladislav.nebesky@ff.cuni.cz`

**Abstract:**
The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebesky in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize properties of the interval function.

**Keywords:** graphs, distance, interval function, geodetic graphs

**Classification (MSC2000):** 05C12, 05C75

**Full text of the article:**

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