  For a graph $G$ and a non-zero real number $\alpha$, the graph invariant
$S_{\alpha}(G)$ is the sum of the $\alpha^{th}$ power of the non-zero signless
Laplacian eigenvalues of $G$. In this paper, we obtain the sharp bounds of
$S_{\alpha}(G)$ for a connected bipartite graph $G$ on $n$ vertices and a
connected graph $G$ on $n$ vertices having a connectivity less than or equal to
$k$, respectively, and propose some open problems for future research.
