×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] Brouwer, A.E.; Cohen, A.M.; Neumaier, A., Distance-regular graphs, (1989.), Springer Heidelberg
[2] Brouwer, A.E.; Mesner, D.M., The connectivity of strongly regular graphs, European J. combin., 6, 215-216, (1985) · Zbl 0607.05045
[3] Brualdi, R.A.; Ryser, H.J., Combinatorial matrix theory, (1991.), Cambridge Univ. Press
[4] Chartrand, G.; Goldsmith, D.L.; Schuster, S., A sufficient condition for graphs with 1-factors, Colloq. math., 41, 339-344, (1979) · Zbl 0447.05035
[5] Cvetković, D.M.; Doob, M.; Sachs, H., Spectra of graphs, (1995), Johann Abrosius Barth Verlag, (First edition: Deutscher Verlag der Wissenschaften, Berlin 1980; Academic Press, New York 1980). · Zbl 0824.05046
[6] G. Frobenius, Über zerlegbare Determinanten, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1917) 456-477 · JFM 46.0144.05
[7] Haemers, W.H., Interlacing eigenvalues and graphs, Linear algebra appl., 226-228, 593-616, (1995) · Zbl 0831.05044
[8] Hall, P., On representations of subsets, J. London math. soc., 10, 26-30, (1935) · Zbl 0010.34503
[9] König, D., Über graphen und ihre anwendung auf determinantentheorie und mengenlehre, Math. ann., 77, 453-465, (1916) · JFM 46.0146.03
[10] König, D., Graphok és matrixok (graphs and matrices), Matematikai és fizikai lapok, 38, 116-119, (1931)
[11] Tutte, W.T., The factorizations of linear graphs, J. London math. soc., 22, 107-111, (1947) · Zbl 0029.23301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.