A nodal domain theorem and a higher-order Cheeger inequality for the graph p-Laplacian
EMS Journal of Spectral Theory, vol. 8, pp. 883–908, 2018
We consider the nonlinear graph $p$-Laplacian and its set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle. We prove a nodal domain theorem for the graph $p$-Laplacian for any $p\geq 1$. While for $p>1$ the bounds on the number of weak and strong nodal domains are the …