An eigenvector interlacing property of graphs that arise from trees by Schur complementation of the Laplacian. Academic Article uri icon

abstract

  • The literature is replete with rich connections between the structure of a graph G = (V, E) and the spectral properties of its Laplacian matrix L. This paper establishes similar connections between the structure of G and the Laplacian L* of a second graph G*. Our interest lies in L* that can be obtained from L by Schur complementation, in which case we say that G* is partially-supplied with respect to G. In particular, we specialize to where G is a tree with points of articulation r R and consider the partially-supplied graph G* derived from G by taking the Schur complement with respect to R in L. Our results characterize how the eigenvectors of the Laplacian of G* relate to each other and to the structure of the tree.

published proceedings

  • Linear Algebra Appl

altmetric score

  • 5.456

author list (cited authors)

  • Griffing, A. R., Lynch, B. R., & Stone, E. A.

citation count

  • 3

complete list of authors

  • Griffing, Alexander R||Lynch, Benjamin R||Stone, Eric A

publication date

  • February 2013