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Trees with a large Laplacian eigenvalue multiplicity
In this paper, we study the multiplicity of the Laplacian eigenvalues of
trees. It is known that for trees, integer Laplacian eigenvalues larger than
are simple and also the multiplicity of Laplacian eigenvalue has been
well studied before. Here we consider the multiplicities of the other
(non-integral) Laplacian eigenvalues. We give an upper bound and determine the
trees of order that have a multiplicity that is close to the upper bound
, and emphasize the particular role of the algebraic
connectivity.Comment: 11 pages, 5 figure