Graphs with minimum spanner \(\varsigma(G)\geq2\rho-1\). (English) Zbl 1248.05195
Summary: 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.
MSC:
05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
05C35 | Extremal problems in graph theory |
05C60 | Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) |
05C90 | Applications of graph theory |