Graphs with Minimum Spanner $\xi (G)\ge 2\rho -1$

Abstract

The parameter $t$ of a tree $t$-spanner of a graph is always bounded by $2\lambda$ where $\lambda$ is the diameter of the graph. In this paper, we establish a sufficient condition for graphs to have the minimum spanner at least $2\rho –1$ where $\rho$ is the radius. We also obtain a characterization for tree $3$-spanner admissible chordal graphs in terms of tree $3$-spanner admissibility of certain subgraphs.