The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits
the possible geometric multiplicities of the eigenvalues, which are far more limited by this …

Using the method of seeds and branch duplication, it is shown that for every tree of diameter,
there is an Hermitian matrix with as few as distinct eigenvalues (a known lower bound). For …

Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of
the fact recent analysis shows that the geometric multiplicity theory for the eigenvalues of …

Given a tree T, let q (T) be the minimum number of distinct eigenvalues in a symmetric matrix
whose underlying graph is T. It is well known that q (T)≥ d (T)+ 1, where d (T) is the …

It is known that the minimum number of distinct eigenvalues c (T) of a symmetric matrix
whose graph is a given tree T is at least the diameter d (T) of that tree. However, the disparity …