Abstract
A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.
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Da Fonseca, C.M. On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. Annali di Matematica 187, 251–261 (2008). https://doi.org/10.1007/s10231-007-0044-3
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DOI: https://doi.org/10.1007/s10231-007-0044-3