The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑u,v∈V(G) d(u, v) where dG(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 SWk(G) of G is defined by [...] . Expressions for SWk for some special graphs are obtained. We also give sharp upper and lower bounds of SWk 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.
@article{bwmeta1.element.doi-10_7151_dmgt_1868,
author = {Xueliang Li and Yaping Mao and Ivan Gutman},
title = {The Steiner Wiener Index of A Graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {455-465},
zbl = {1334.05027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1868}
}
Xueliang Li; Yaping Mao; Ivan Gutman. The Steiner Wiener Index of A Graph. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 455-465. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1868/