Strong Distance in Strong Digraphs
For two vertices $u$ and $v$ in
a strong oriented graph $D$ of order $n \geq 3$,
the strong distance $\sd(u, v)$
between $u$ and $v$ is the minimum size
of a strong subdigraph of $D$ containing $u$ and $v$.
For a vertex $v$ of $D$, the strong eccentricity $\se(v)$ is
the strong distance between $v$ and a vertex farthest from $v$.
The minimum strong eccentricity among the vertices of
$D$ is the strong radius $\srad D$,
and the maximum strong eccentricity is its strong diameter
$ \sdiam D$. It is shown that every pair $r, d$ of integers
with $3 \leq r \leq d \leq 2r$ is realizable as the strong
radius and strong diameter of some strong oriented graph.
Also, for every strong oriented graph $D$ of order $n \geq3$,
it is shown that $\sdiam (D) \leq \lfloor{5(n-1)/3}\rfloor$.
Furthermore,
for every integer $n \geq 3$, there exists a
strong oriented graph $D$ of order $n$ such that
$\sdiam (D) = \lfloor{5(n-1)/3}\rfloor$.