On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree

Abstract

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.