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Displaying similar documents to “New proof of a characterization of geodetic graphs”

The interval function of a connected graph and a characterization of geodetic graphs

Ladislav Nebeský (2001)

Mathematica Bohemica

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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...

Route systems of a connected graph

Ladislav Nebeský (1994)

Mathematica Bohemica

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The concept of a route system was introduced by the present author in [3].Route systems of a connected graph G generalize the set of all shortest paths in G . In this paper some properties of route systems are studied.