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Laplacian graph eigenvectors

✍ Scribed by Russell Merris

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 1015 KB
Volume: 278
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10080-5

No coin nor oath required. For personal study only.

✦ Synopsis

If G is a graph, its Laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The main thrust of the present article is to prove several Laplacian eigenvector "principles" which in certain cases can be used to deduce the effect on the spectrum of contracting, adding or deleting edges and/or of coalescing vertices. One application is the construction of two isospectral graphs on 11 vertices having different degree sequences, only one of which is bipartite, and only one of which is decomposable.

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