  The topological property of SrRu$_2$O$_6$ and isostructural CaOs$_2$O$_6$
under various strain conditions is investigated using density functional
theory. Based on an analysis of parity eigenvalues, we anticipate that a
three-dimensional strong topological insulating state should be realized when
band inversion is induced at the A point in the hexagonal Brillouin zone. For
SrRu$_2$O$_6$, such a transition requires rather unrealistic tuning, where only
the $c$ axis is reduced while other structural parameters are unchanged.
However, given the larger spin-orbit coupling and smaller lattice constants in
CaOs$_2$O$_6$, the desired topological transition does occur under uniform
compressive strain. Our study paves a way to realize a topological insulating
state in a complex oxide, which has not been experimentally demonstrated so
far.
