  L.H. Feng at el \cite{feng4} present sufficient conditions based on spectral
radius for a graph with large minimum degree to be $s$-path-coverable and
$s$-Hamiltonian. Motivated by this study, in this paper, we give the sufficient
conditions for a graph with large minimum degree to be $s$-connected,
$s$-edge-connected, $\beta$-deficient, $s$-path-coverable, $s$-Hamiltonian and
$s$-edge-Hamiltonian in terms of spectral radius of its complement.
