In this paper we investigate the relation between eigenvalue distribution and graph structure of two classes of graphs: the (m, k)-stars and l-dependent graphs. We give conditions on the topology and edge weights 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 and the physical relevance of the results is shortly discussed. (C) 2018 Elsevier Inc. All rights reserved.
On the multiplicity of Laplacian eigenvalues and Fiedler partitions / Andreotti, E; Remondini, D; Servizi, G; Bazzani, A. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - ELETTRONICO. - 544:(2018), pp. 206-222. [10.1016/j.laa.2018.01.009]
On the multiplicity of Laplacian eigenvalues and Fiedler partitions
ANDREOTTI, ELEONORA
;Remondini, D
;Servizi, G;Bazzani, A
2018
Abstract
In this paper we investigate the relation between eigenvalue distribution and graph structure of two classes of graphs: the (m, k)-stars and l-dependent graphs. We give conditions on the topology and edge weights 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 and the physical relevance of the results is shortly discussed. (C) 2018 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
