Spectral conditions of complement for some graphical properties

Abstract

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.