  We investigate the ground-state properies of the $K-\Gamma$ model on a
honeycomb lattice using series expansions and numerical exact diagonalizations,
where the model includes Kitaev ($K$) and symmetric off-diagonal ($\Gamma$)
interactions. Starting from the weakly interacting dimers on the specific bond,
we strengthen the interdimer interactions to the isotropically interacting
system. We show that depending on $\Gamma$ and $K$, the dimer state survives up
to the isotropically interacting system, where the phase transition occurs, or
obeys a phase transition to a magnetically ordered state at an anisotropic
interaction. The results are summarized in the phase diagram. We also show that
the Kekul\'{e} dimerized state is unstable in the isotropic $K-\Gamma$ model.
