Geodesic
A characterization of the interval function of a (finite or infinite) connected graph
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 635-642.

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By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.
Classification : 05C12
Keywords: distance in a graph; interval function 
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     title = {A characterization of the interval function of a (finite or infinite) connected graph},
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Nebeský, Ladislav. A characterization of the interval function of a (finite or infinite) connected graph. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 635-642. http://geodesic.mathdoc.fr/item/CMJ_2001__51_3_a13/