We give an upper (resp. a lower) bound on the largest (resp. the least) eigenvalue of the signless Laplacian matrix of a Hamiltonian graph. These bounds are applied to obtain sufficient spectral conditions for the non-existence of Hamiltonian cycles. Under certain additional assumptions we provide a polynomial time decisive spectral criterion for the Hamiltonicity of a given graph with sufficiently large minimum vertex degree.

中文翻译：

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哈密​​顿图的无符号拉普拉斯特征值的界

我们给出了哈密顿图的无符号拉普拉斯矩阵的最大（最小）特征值的上（下）界。应用这些界限是为了获得不存在哈密顿循环的足够谱条件。在某些额外的假设下，我们为具有足够大的最小顶点度的给定图的哈密顿性提供了多项式时间决定性谱标准。