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Laplacian graph eigenvectors. (English) Zbl 0932.05057
Summary: 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 artilce 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.

##### MSC:
 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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##### References:
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