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On the sum of all distances in a graph or digraph

✍ Scribed by Ján Plesník

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
870 KB
Volume
8
Category
Article
ISSN
0364-9024

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✦ Synopsis

The transmission of a graph or digraph G is the sum of all distances in G. StFict bounds on the transmission are collected and extended for several classes of graphs and digraphs. For example, in the class of 2connected or Z-edge-mnnected graphs of order n, the maximal transmission is realized only by the cycle C,. 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.

c + ( u ) = c d ( U , X ) ,

X€V(G)

📜 SIMILAR VOLUMES

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Let G=( V, E) be a digraph with diameter D # 1. For a given integer 1 t. The t-distance edge-connectivity of G is defined analogously. This paper studies some results on the distance connectivities of digraphs and bipartite digraphs. These results are given in terms of the parameter I, which can be

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## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _