Geodesic
On the multiplicity of Laplacian eigenvalues of graphs
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 689-698.

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In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.
Classification : 05C50
Keywords: Laplacian eigenvalue; multiplicity; tree; characteristic polynomial 
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     author = {Guo, Ji-Ming and Feng, Lin and Zhang, Jiong-Ming},
     title = {On the multiplicity of {Laplacian} eigenvalues of graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {689--698},
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     zbl = {1224.05297},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a7/}
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Guo, Ji-Ming; Feng, Lin; Zhang, Jiong-Ming. On the multiplicity of Laplacian eigenvalues of graphs. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 689-698. http://geodesic.mathdoc.fr/item/CMJ_2010__60_3_a7/