- Tytuł:
- Inverse Problem on the Steiner Wiener Index
- Autorzy:
-
Li, Xueliang
Mao, Yaping
Gutman, Ivan - Powiązania:
- https://bibliotekanauki.pl/articles/31342440.pdf
- Data publikacji:
- 2018-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
distance
Steiner distance
Wiener index
Steiner Wiener 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_G(u, v) $, where $ d_G(u, v) $ is the distance (the length a shortest path) between the vertices $u$ and $v$ in $G$. For $ S \subseteq 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 $ SW_k(G) $ of $G$ is defined as $ SW_k(G)= \Sigma_{ S \subseteq V(G) \ |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 \ge k$ such that $ SW_k(G) = w$ (or $ SW_k(T) = w$)? In this paper, we give some solutions to this problem.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 83-95
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł