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Keywords:
Laplacian eigenvalue; multiplicity; tree; characteristic polynomial
Laplacian eigenvalue; multiplicity; tree; characteristic polynomial
Summary:
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.
References:
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