A note on the Steiner -diameter of a graph. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Mao, Yaping; Melekian, Christopher; Cheng, Eddie
• Is Part Of: International journal of computer mathematics. Volume 3:Issue 1(2018)
• Page Start: 41
• Page End: 46
• Publication Date: 2018-01-02
• Subjects: Diameter -- Steiner tree -- Steiner k-diameter; 05C05 -- 05C12 -- 05C76; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2018.1441186
• Languages: English
• ISSNs: 2379-9927

Abstract

ABSTRACT: The Steiner distance of a graph, introduced by Chartrand in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and, the Steiner distance among the vertices of S is the minimum size among all connected subgraphs whose vertex sets contain S . Let n and k be two integers with . Then the Steiner k -eccentricity of a vertex v of G is defined by . Furthermore, the Steiner k-diameter of G is . In 2011, Chartrand et al. showed that . In this paper, graphs with for are characterized.