The Steiner Wiener Index of A Graph

The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑ d(u, v) where d (u, v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical gr...

Full description

Saved in:
Bibliographic Details
Published inDiscussiones Mathematicae. Graph Theory Vol. 36; no. 2; pp. 455 - 465
Main Authors Li, Xueliang, Mao, Yaping, Gutman, Ivan
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.05.2016
University of Zielona Góra
Subjects
distance
Steiner distance
Steiner Wiener k- index
Wiener index
Online AccessGet full text

Cover

More Information
Summary:The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑ d(u, v) where d (u, v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph whose vertex set is S. We now introduce the concept of the Steiner Wiener index of a graph. The Steiner k-Wiener index SW (G) of G is defined by . Expressions for SW for some special graphs are obtained. We also give sharp upper and lower bounds of SW of a connected graph, and establish some of its properties in the case of trees. An application in chemistry of the Steiner Wiener index is reported in our another paper.
ISSN:1234-3099
2083-5892
DOI:10.7151/dmgt.1868