The Steiner Wiener Index of A Graph

• Autorzy: Xueliang Li , Yaping Mao , Ivan Gutman
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

distance; Steiner distance; Wiener index; Steiner Wiener k- index

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 2
• Strony: 455-465

Daty

wydano

2016-05-01

otrzymano

2014-12-27

poprawiono

2015-08-13

zaakceptowano

2015-08-13

online

2016-04-15

Twórcy

autor

Xueliang Li

• Center for Combinatorics and LPMC Nankai University, Tianjin 300071, China

autor

Yaping Mao

• Department of Mathematics Qinghai Normal University Qinghai 810008, China

autor

Ivan Gutman

• Faculty of Science P.O. Box 60, 34000 Kragujevac, Serbia and State University of Novi Pazar, Novi Pazar, Serbia

Identyfikatory

DOI

10.7151/dmgt.1868