Eigenvalues and perfect matchings. (English) Zbl 1056.05097

Summary: We give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix. We also show that a distance-regular graph of degree \(k\) is \(k\)-edge-connected.


05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05E30 Association schemes, strongly regular graphs
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