### On Strong Distance in Strong Oriented Graphs}

For two vertices \$u\$ and \$v\$ in a nontrivial strong oriented graph \$D\$, 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\$. The strong radius and strong diameter of a strong tournament are investigated. The strong center (strong periphery) of a strong oriented graph \$D\$ is the subdigraph of \$D\$ induced by those vertices of strong eccentricity \$\srad(D)\$ (\$\sdiam (D)\$). It is shown that every oriented graph is the strong center of some strong oriented graph. A strong oriented graph \$D\$ is called strongly self-centered if \$D\$ is its own strong center. For every integer \$r \geq 3\$, there exist infinitely many strongly self-centered oriented graphs of strong radius \$r\$. The problem of determining those oriented graphs that are strong peripheries of strong oriented graphs is studied.