Nodal domain count for the generalized graph p-Laplacian

Inspired by the linear Schrödinger operator, we consider a generalized p-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this with particular attention to nodal domain count its eigenfunctions. Just like one-dimensional continuous p-Laplacian, prove variational spectrum forests is entire spectrum. Moreover, show how transfer Weyl's inequalities for Laplacian nonlinear case upper lower bounds number domains every eigenfunction generic graphs, including eigenpairs. In particular, when applied p=2, in addition recovering well-known features, provide novel operator.