We prove discrete versions of nodal domain theorems; in particular, an eigenvector corresponding to the sth smallest eigenvalue of a graph Laplacian has at most s nodal domains. We compare our results to those of Courant and Pleijel on nodal domains of continuous Laplacians, and to those of Fiedler on non-negative regions of graph Laplacians.
|Original language||English (US)|
|Number of pages||10|
|Journal||Linear Algebra and Its Applications|
|State||Published - Jun 15 1999|
Bibliographical noteFunding Information:
*Corresponding author. E-mail: firstname.lastname@example.org 1 E-mail: email@example.com 2 Partially supported by a Sloan Foundation Fellowship.
- Graph Laplacian
- Nodal domain