## On the relative position of multiple eigenvalues in the spectrum of an
Hermitian matrix with a given graph

Charles R. Johnson, António Leal Duarte, Carlos M. Saiago, Brian D. Sutton,
and Andrew J. Witt
*Linear Algebra Appl.* 363 (2003), 147–159.

For Hermitian matrices, whose graph is a given tree, the relationships among vertex
degrees, multiple eigenvalues and the relative position of the underlying eigenvalues
in the ordered spectrum are discussed in detail. In the process, certain aspects of
special vertices, whose removal results in an increase in multiplicity, are
investigated.

home