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

Abstract

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.