engleski

Wiener number of directed graphs and its relation to the oriented network design problem

The modified Wiener number on trees has been defined recently as a sum of modified edge contributions, which are simply the number of shortest paths traversing the edge to the power of alfa. We study digraphs with minimal value for one possible modification of the Wiener number for directed graphs. For this generalization. For digraphs with unique shortest paths we provide minimal digraphs for alfa <= 0 and alfa >= 1, and give some partial results for alfa element (0, 1).

directed graph; Wiener number; network design

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