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Displaying similar documents to “A theorem for an axiomatic approach to metric properties of 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...

A characterization of the interval function of a (finite or infinite) connected graph

Ladislav Nebeský (2001)

Czechoslovak Mathematical Journal

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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...

A Note on the Interval Function of a Disconnected Graph

Manoj Changat, Ferdoos Hossein Nezhad, Henry Martyn Mulder, N. Narayanan (2018)

Discussiones Mathematicae Graph Theory

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In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.

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.