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arXiv · 1707.04204

On the multiplicity of Laplacian eigenvalues and Fiedler partitions

Eleonora Andreotti·Armando Bazzani·Daniel Remondini·Graziano Servizi
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Abstract

In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on graphs with (m,k)-star subgraphs is feasible, keeping the same eigenvalues with reduced multiplicity. Moreover, some useful eigenvectors properties are derived up to a product with a suitable matrix. Finally, we relate these results with Fiedler spectral partitioning of the graph. The physical relevance of the results is shortly discussed.

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Eleonora Andreotti, Armando Bazzani, Daniel Remondini, Graziano Servizi. 2017-07-13. On the multiplicity of Laplacian eigenvalues and Fiedler partitions. https://arxiv.org/abs/1707.04204

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