A note on the Steiner -diameter of a graph. Issue 1 (2nd January 2018) - Mao, Yaping; Melekian, Christopher; Cheng, Eddie
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.