# The Steiner Wiener Index of A Graph

Xueliang Li; Yaping Mao; Ivan Gutman

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 2, page 455-465
- ISSN: 2083-5892

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topXueliang 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 -

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