Abstract:
We characterize the possible lists of multiplicities occurring among the eigenvalues of a real symmetric (or Hermitian) matrix whose graph is one of K_n, K_n less an edge, or both possibilities for K_n less two edges. The lists are quite different from those for trees. Some construction techniques are developed here and additional results with more missing edges are given, including the case of several independent edges. (This is a joint work with C. R. Jonhson) |