- Tytuł:
- The Steiner Wiener Index of A Graph
- Autorzy:
-
Li, Xueliang
Mao, Yaping
Gutman, Ivan - Powiązania:
- https://bibliotekanauki.pl/articles/31340916.pdf
- Data publikacji:
- 2016-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
distance
Steiner distance
Wiener index
Steiner Wiener k- index - Opis:
- The Wiener index $ W(G) $ of a connected graph $G$, introduced by Wiener in 1947, is defined as $ W(G) = \Sigma_{ u,v \in V(G) } d(u, v) $ where $ d_G(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 \subseteq 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 $ SW_k(G) $ of $ G $ is defined by $ \Sigma_{ S \subseteq V(G) \ |S| = k } \ d(S) $. Expressions for $ SW_k $ for some special graphs are obtained. We also give sharp upper and lower bounds of $ SW_k $ 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 455-465
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł