A characterization of the set of all shortest paths in a connected graph

Ladislav Nebeský

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Visibilities and sets of shortest paths in a connected graph

Ladislav Nebeský (1995)

Czechoslovak Mathematical Journal

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Characterizing the interval function of a connected graph

Ladislav Nebeský (1998)

Mathematica Bohemica

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As was shown in the book of Mulder [4], the interval function is an important tool for studying metric properties of connected graphs. An axiomatic characterization of the interval function of a connected graph was given by the present author in [5]. (Using the terminology of Bandelt, van de Vel and Verheul [1] and Bandelt and Chepoi [2], we may say that [5] gave a necessary and sufficient condition for a finite geometric interval space to be graphic). In the present paper, the result...

Circular distance in directed graphs

Bohdan Zelinka (1997)

Mathematica Bohemica

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Circular distance $d^{\circ} (x, y)$ between two vertices $x$ , $y$ of a strongly connected directed graph $G$ is the sum $d (x, y) + d (y, x)$ , where $d$ is the usual distance in digraphs. Its basic properties are studied.