Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Steiner Wiener index

Sortuj według:

Ogranicz wyniki do:

Inverse Problem on the Steiner Wiener Index

100%

Li X., Mao Y., Gutman I.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

83-95

The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) =∑u,v∈V (G) dG(u, v), where dG(u, v) is the distance (the length a shortest path) between the vertices u and v in G. For S ⊆ V (G), the Steiner distance d(S) of the vertices of S, introduced by Chartrand et al. in 1989, is the minimum size of a connected subgraph of G whose vertex set contains S. The k-th Steiner Wiener index SWk(G) of G is defined as [...] SWk(G)=∑S⊆V(G)|S|=kd(S) $SW_k (G) = \sum\nolimits_{\mathop {S \subseteq V(G)}\limits_{|S| = k} } {d(S)}$ . We investigate the following problem: Fixed a positive integer k, for what kind of positive integer w does there exist a connected graph G (or a tree T) of order n ≥ k such that SWk(G) = w (or SWk(T) = w)? In this paper, we give some solutions to this problem.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Gutman I.

1 Li X.

1 Mao Y.

1 2018

Wyniki wyszukiwania

Inverse Problem on the Steiner Wiener Index