Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 325, Issue 1-3, Pages 71-74Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/S0024-3795(00)00333-5
Keywords
maximum matching; matching number; Laplacian spectrum
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Let G be a graph, its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. In this paper, we generalize a result in (R. Merris, Port. Math.48 (3) 1991) and obtain the following result: Let G be a graph and M(G) be a maximum matching in G. Then the number of edges in M(G) is a lower bound for the number of Laplacian eigenvalues of G exceeding 2. (C) 2001 Elsevier Science Inc. All rights reserved. AMS classification: 05c50.
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