  We prove that for a one-ended hyperbolic graph $X$, the size of the quotient
$X/G$ by a group $G$ acting freely and cocompactly bounds from below the number
of simplices in an Eilenberg-MacLane space for $G$. We apply this theorem to
show that one-ended hyperbolic cubulated groups (or more generally, one-ended
hyperbolic groups with globally stable cylinders \`a la Rips-Sela) cannot
contain isomorphic finite-index subgroups of different indices.
