Geodesic
The interval function of a connected graph and a characterization of geodetic graphs
Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 247-254.

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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 Nebeský 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.
DOI : 10.21136/MB.2001.133909
Classification : 05C12, 05C75
Keywords: graphs; distance; interval function; geodetic graphs 
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Nebeský, Ladislav. The interval function of a connected graph and a characterization of geodetic graphs. Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 247-254. doi : 10.21136/MB.2001.133909. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.133909/

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