  A vertex coloring of a strong digraph $D$ is a \emph{strong
vertex-monochromatic connection coloring (SVMC-coloring)} if for every pair $u,
v$ of vertices in $D$ there exists an $(u,v)$-path having all its internal
vertices of the same color. Let $smc_v(D)$ denote the maximum number of colors
used in an SVMC-coloring of a digraph $D$. In this paper we determine the value
of $smc_v(D)$, whenever $D$ is the line digraph of a digraph. Also, if $T$ is a
tournament, we give conditions to find the exact value of $smc_v(T)$.
