  In this work, we systematically investigate the dibaryons with charm number
$C$=1 and strangeness number $S$=$\pm$ 1 from the interactions of a charmed
baryon and a strange baryon $\Lambda_c\Lambda$, $\Lambda_c\Sigma^{(*)}$,
$\Sigma_c^{(*)}\Lambda$, and $\Sigma^{(*)}_c\Sigma^{(*)}$, and corresponding
interactions of a charmed baryon and an antistrange baryon
$\Lambda_c\bar{\Lambda}$, $\Lambda_c\bar{\Sigma}^{(*)}$,
$\Sigma^{(*)}_c\bar{\Lambda}$, and $\Sigma^{(*)}_c\bar{\Sigma}^{(*)}$. With the
help of the effective Lagrangians with $SU(3)$, heavy quark, and chiral
symmetries, the potentials of the interactions considered are constructed by
light meson exchanges. To search for the possible molecules, the quasipotential
Bethe-Salpeter equation with the interaction potential kernel is solved to find
poles from scattering amplitude. The results suggest that attractions widely
exist in charmed-strange system with $C$=1 and $S$=$-1$. The $S$-wave bound
states can be produced from most of the channels. Few bound states are also
produced from the charmed-antistrange interactions. Couple-channel effect are
considered in the current work to discuss the couplings of the molecular states
to the channels considered. More experimental research for these
charmed-strange dibaryons are suggested.
