In this paper, a graph theoretic analog to the celebrated Faber-Krahn inequality for the first eigenvalue of the Dirichlet problem of the Laplacian for a bounded domain in the Euclidean space is shown. Namely, the optimal estimate of the first eigenvalue of the Dirichlet boundary problem of the combinatorial Laplacian for a graph with boundary is given.
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)