On the Steiner 4-Diameter of Graphs.

The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou 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 dG(S) among the vertices of S is the minimum size among all connected subgraphs whose vertex sets contain S. Let n, k be two integers with 2 ≤ k ≤ n. Then the Steiner k-eccentricity ek(v) of a vertex v of G is defined by . Furthermore, the Steiner k-diameter of G is . In 2011, Chartrand, Okamoto and Zhang showed that k − 1 ≤ sdiamk(G) ≤ n − 1. In this paper, graphs with sdiam4( G) = 3, 4, n − 1 are characterized, respectively. [ABSTRACT FROM AUTHOR]