The interval function of a connected graph and a characterization of geodetic graphs
- 1 January 2001
- journal article
- Published by Institute of Mathematics, Czech Academy of Sciences in Mathematica Bohemica
- Vol. 126 (1) , 247-254
- https://doi.org/10.21136/mb.2001.133909
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 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.Keywords
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