  In this research, the strong coupling constants of the $D^*D_s^*K$,
$D_1D_{s1}K$, $D^*D_sK$ and $D_1D_{s0}^*K$ vertices are evaluated, using the
three-point QCD sum rules. In order to calculate the coupling constant of each
vertex, either the kaon or the charmed meson is considered as the off-shell
particle. The basic $g$ parameter, in the heavy quark effective theory, is
related to the coupling constants of $D^*D_s^*K$ and $D^*D_sK$. Our obtained
value for $g$ parameter is $0.24\pm 0.09$, which is in good agreement with the
lower limits of the other existing predictions.
