Some remarks on Wiener index of oriented graphs

Some remarks on Wiener index of oriented graphs

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Article ID: iaor201530239
Volume: 273
Start Page Number: 631
End Page Number: 636
Publication Date: Jan 2016
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: graphs
Abstract:

In this paper, we study the Wiener index (i.e., the total distance or the transmission number) of not necessarily strongly connected digraphs. In order to do so, if there is no directed path from u to v, we follow the convention d ( u , v ) = 0 , equ1 which was independently introduced in several studies of directed networks. Under this assumption we naturally generalize the Wiener theorem, as well as a relation between the Wiener index and betweenness centrality to directed graphs. We formulate and study conjectures about orientations of undirected graphs which achieve the extremal values of Wiener index.

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