Some remarks on Wiener index of oriented graphs

被引：21

作者：

Knor, Martin ^{[1
]}

Skrekovski, Riste ^{[2
,3
,4
,5
]}

Tepeh, Aleksandra ^{[2
,6
]}

机构：

[1] Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Bratislava, Slovakia

[2] Fac Informat Studies, Novo Mesto, Slovenia

[3] Inst Math Phys & Mech, Ljubljana, Slovenia

[4] Univ Ljubljana, Fac Math & Phys, Ljubljana 61000, Slovenia

[5] Univ Primorska, FAMNIT, Koper, Slovenia

[6] Univ Maribor, Fac Elect Engn & Comp Sci, Maribor, Slovenia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 273卷

关键词：

Wiener index; Average graph distance; Total distance; Directed graph; Betweenness centrality; Social networks; AVERAGE DISTANCE; MEAN DISTANCE;

D O I：

10.1016/j.amc.2015.10.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, 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. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：631 / 636

页数：6

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