MATHEMATICA BOHEMICA, Vol. 126, No. 1, pp. 247-254 (2001)

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:

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

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