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1984•Journal of Graph TheoryRequires access

On the sum of all distances in a graph or digraph

Ján Plesnı́k

Open publisher page 260 citations

Abstract

Abstract The transmission of a graph or digraph G is the sum of all distances in G. Strict bounds on the transmission are collected and extended for several classes of graphs and digraphs. For example, in the class of 2‐connected or 2‐edge‐connected graphs of order n, the maximal transmission is realized only by the cycle Cn. The independence of the transmission on the diameter or radius is shown. Remarks are also given about the NP‐hardness of some related algorithmic problems.

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Abstract The transmission of a graph or digraph G is the sum of all distances in G. Strict bounds on the transmission are collected and extended for several classes of graphs and digraphs. For example, in the class of 2‐connected or 2‐edge‐connected graphs of order n, the maximal transmission is realized only by the cycle Cn. The independence of the transmission on the diameter or radius is shown. Remarks are also given about the NP‐hardness of some related algorithmic problems.

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Available abstract

Abstract The transmission of a graph or digraph G is the sum of all distances in G. Strict bounds on the transmission are collected and extended for several classes of graphs and digraphs. For example, in the class of 2‐connected or 2‐edge‐connected graphs of order n, the maximal transmission is realized only by the cycle Cn. The independence of the transmission on the diameter or radius is shown. Remarks are also given about the NP‐hardness of some related algorithmic problems.

Key concepts: Combinatorics, Digraph, Mathematics, Independence number, Graph, Discrete mathematics

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