Extremal Graph Theory for Metric Dimension and Diameter 1

Let Gβ,D be the set of graphs with metric dimension β and diameter D. The first contribution is to characterize the graphs in Gβ,D with order β+D for all values of β and D. The second contribution is to determine the maximum order of a graph in Gβ,D for all values of D and β. Only a weak upper bound was previously known.