  A connected graph $G$ is said to be $k$-connected if it has more than $k$
vertices and remains connected whenever fewer than $k$ vertices are deleted. In
this paper, for a connected graph $G$ with sufficiently large order, we present
a tight sufficient condition for $G$ with fixed minimum degree to be
$k$-connected based on the $Q$-index. Our result can be viewed as a spectral
counterpart of the corresponding Dirac type condition.
