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 signlessLaplacian 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 aconnected graph $G$ on $n$ vertices having a connectivity less than or equal to$k$, respectively, and propose some open problems for future research.
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机译：对于图$ G $和非零实数$ \ alpha $，图不变$ S _ {\ alpha}（G）$是非零值$ \ alpha ^ {th} $幂的和$ G $的拉普拉斯特征值。在本文中，我们获得连通度小于或的连通二部图$ G $在$ n $顶点上的连通图$ G $和连通图$ G $在$ n $顶点上的连通图$ G $的尖锐边界$ S _ {\ alpha}（G）$分别等于$ k $，并提出了一些未解决的问题，以供将来研究。
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