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Questions related to the spectrum of graphs, defined using one of the possible variants of the discrete Laplace operator or Laplacian matrix. See https://en.wikipedia.org/wiki/Discrete_Laplace_operator

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Multiplicity of the smallest non-zero Laplacian eigenvalue for tree graphs

How accurate is the following statement: "For tree graphs, the multiplicity of the smallest non-zero eigenvalue $\lambda_2$ of the Laplacian is 1." If not valid, in which cases does it fail to hold? I …
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