A Short Note on the Large Steiner s-Diameter of Graphs

In a graph \( G \), the Steiner distance \( d(S) \) of the vertex subset \( S \subseteq V(G) \) is the minimum size among all connected subgraphs whose vertex sets contain \( S \). The Steiner \( k \)-diameter of a connected graph \( G \) is the maximum \( d(S) \) among all \( k \)-element vertex subsets \( S \subseteq V(G) \).

In this paper, we examine the Steiner \( k \)-diameter for large \( k \) and then discuss the applications of the results.