Displaying similar documents to “A new proof of a characterization of the set of all geodesics in a connected graph”

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...

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...

The all-paths transit function of a graph

Manoj Changat, Sandi Klavžar, Henry Martyn Mulder (2001)

Czechoslovak Mathematical Journal

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A transit function R on a set V is a function R V × V → 2 V satisfying the axioms u ∈ R ( u , v ) , R ( u , v ) = R ( v , u ) and R ( u , u ) = { u } , for all u , v ∈ V . The all-paths transit function of a connected graph is characterized by transit axioms.