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The star matching number and (signless) Laplacian eigenvalues. (Chinese. English summary) Zbl 1340.05165

Summary: Let \(G\) be a simple graph, and \(s\leqslant 3\) be an integer. In this paper, if \(G\) is a connected graph with order \(n\) and \(K_{1, s}\)-matching number \(m(G)\), such that \(n>(s+1)m(G)\), then the \(m(G)\)-th largest Laplacian eigenvalue \(\mu_{m(G)}>s+1\). And this result also holds for signless spectra. As an application, some \(Q\)-eigenvalue conditions which can determine the Hamiltonicity of a graph are listed.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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