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We showed that: If $G$ is a non-bipartite connected graph, then $q(G)\geqslant \frac{1}{n(D+1)}$, where $g(G)$ is the least $Q$-eigenvalue of $G$, and $D$ is the diameter of $G$. Some relations between the least $Q$-eigenvalue of $G$ and that of its subgraph were given.
{1}GRONE R, MERRIS R, SUNDER V S. The Laplacian spectrum of a graph[J]. SIAM J Matrix Anal, 1990(2): 218-238.{2}CVETKOVI\'C D, ROWLINSON P, SLOBODAN K S. Signless Laplacians of finite graphs[J]. Linear Algebra Appl, 2007, 423: 155-171.{3}CVETKOVI\'C D, SLOBODAN K S. Towards a spectral theory of graphs based on signless Laplacian II[J]. Linear Algebra Appl, 2010, 432(9): 2257-2272.{4}DAS K C. On conjectures involving second largest signless Laplacian eigenvalue of graphs[J]. Linear Algebra Appl, 2010, 432(11): 3018-3029.{5}FENG L, LI Q, ZHANG X D. Minimizing the Laplacian spectral radius of trees with given matching number[J]. Linear Multilinear Algebra, 2007, 55: 199-207.{6}CARDOSO D M, CVETKOVI\'C D, ROWLINSON P, et al. A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph[J]. Linear Algebra and its Applications, 2008, 429: 2770-2780.