On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree
The author gives alternative and simpler proofs of some results of \textit{C. R. Johnson} and \textit{A. L. Duarte} [Linear Multilinear Algebra 46, No. 1--2, 139--144 (1999; Zbl 0929.15005)] and \textit{C. R. Johnson} and \textit{C. M. Saiago} [Electron J. Linear Algebra 9, 27--31 (2002; Zbl 0999.15005)] on the minimum number of vertex disjoint paths, occuring as induced subgraphs of a tree \(T\), which cover all the vertices of \(T\). The approach is based on classic results of \textit{O. J. Heilmann} and \textit{E. H. Lieb} [Commun. Math. Phys. 25, 190--232 (1972; Zbl 0228.05131)] from the theory of matching polynomials.
scientific article; zbMATH DE number 5292345
scientific article