A Sharp Lower Bound on the Least Signless Laplacian Eigenvalue of a Graph
Tóm tắt
Let G be a simple graph with n vertices and m edges, and let
$$q_{n}(G)$$
be the least signless Laplacian eigenvalue of G. Recently, Guo, Chen and Yu proved that if
$$n\ge 6$$
, then
$$\begin{aligned} q_{n}(G)\ge \frac{2m}{n-2}-n+1, \end{aligned}$$
which confirms a conjecture proposed by de Lima, Oliveira, de Abreu and Nikiforov. In this note, we present a new proof for the above inequality, where we also completely characterize the case when the equality holds.
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