On Steiner degree distance of trees
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- 作者：Ivan Gutmana ; b ; gutman@kg.ac.rs" class="auth_mail" title="E-mail the corresponding author
- 关键词：Distance (in graph) ; Steiner distance ; Degree distance ; Wiener index
- 刊名：Applied Mathematics and Computation
- 出版年：2016
- 出版时间：20 June 2016
- 年：2016
- 卷：283
- 期：Complete
- 页码：163-167
- 全文大小：293 K
文摘
Let G be a connected graph, and u, v, w its vertices. By du is denoted the degree of the vertex u, by d(u, v) the (ordinary) distance of the vertices u and v, and by d(u, v, w) the Steiner distance of u, v, w. The degree distance DD of G is defined as the sum of terms 
over all pairs of vertices of G. As early as in the 1990s, a linear relation was discovered between DD of trees and the Wiener index. We now consider SDD, the Steiner–distance generalization of DD , defined as the sum of terms over all triples of vertices of G. Also in this case, a linear relation between SDD and the Wiener index could be established.
over all pairs of vertices of G. As early as in the 1990s, a linear relation was discovered between DD of trees and the Wiener index. We now consider SDD, the Steiner–distance generalization of DD , defined as the sum of terms over all triples of vertices of G. Also in this case, a linear relation between SDD and the Wiener index could be established.