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The Steiner Wiener Index of A Graph

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Li X., Mao Y., Gutman I.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

455-465

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Gutman I.

1 Li X.

1 Mao Y.

1 2016

Wyniki wyszukiwania

The Steiner Wiener Index of A Graph