  In 1984, Plesn\'{i}k determined the minimum total distance for given order
and diameter and characterized the extremal graphs and digraphs. We prove the
analog for given order and radius, when the order is sufficiently large
compared to the radius. This confirms asymptotically a conjecture of Chen et
al. We also state an analog of the conjecture of Chen et al for digraphs and
prove it for sufficiently large order.
