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On the spectrum of the normalized graph Laplacian. (English) Zbl 1149.05327
Summary: We investigate how the spectrum of the normalized (geometric) graph Laplacian is affected by operations like motif doubling, graph splitting or joining. The multiplicity of the eigenvalue 1, or equivalently, the dimension of the kernel of the adjacency matrix of the graph is of particular interest. This multiplicity can be increased, for instance, by motif doubling.

MSC:
05C75 Structural characterization of families of graphs
47A75 Eigenvalue problems for linear operators
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