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.
Bibliographical noteFunding Information:
*Corresponding author. E-mail: email@example.com 1 E-mail: firstname.lastname@example.org 2 Partially supported by a Sloan Foundation Fellowship.
- Graph Laplacian
- Nodal domain