The Steiner Wiener Index of A Graph

Xueliang Li, Yaping Mao, and Ivan Gutman. "The Steiner Wiener Index of A Graph." Discussiones Mathematicae Graph Theory 36.2 (2016): 455-465. <http://eudml.org/doc/277120>.

@article{XueliangLi2016,
abstract = {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.},
author = {Xueliang Li, Yaping Mao, Ivan Gutman},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {distance; Steiner distance; Wiener index; Steiner Wiener k- index; Steiner Wiener -index},
language = {eng},
number = {2},
pages = {455-465},
title = {The Steiner Wiener Index of A Graph},
url = {http://eudml.org/doc/277120},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Xueliang Li
AU - Yaping Mao
AU - Ivan Gutman
TI - The Steiner Wiener Index of A Graph
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 455
EP - 465
AB - 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.
LA - eng
KW - distance; Steiner distance; Wiener index; Steiner Wiener k- index; Steiner Wiener -index
UR - http://eudml.org/doc/277120
ER -