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On the maximal signless Laplacian spectral radius of graphs with given matching number. (English) Zbl 1175.05090

Summary: Let \(\mathcal{G}_{n,\beta}\) be the set of simple graphs of order \(n\) with given matching number \(\beta\). In this paper, we investigate the maximal signless Laplacian spectral radius in \(\mathcal{G}_{n,\beta}\) and characterize the extremal graphs with maximal signless Laplacian spectral radius.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C90 Applications of graph theory
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