# Homological eigenvalues of graph $p$-Laplacians

@inproceedings{Zhang2021HomologicalEO, title={Homological eigenvalues of graph \$p\$-Laplacians}, author={Dong Zhang}, year={2021} }

We introduce the homological eigenvalues of the graph p-Laplacian ∆p, and we prove that for any homological eigenvalue λ(∆p), the functions p(2λ(∆p)) 1 p and 2λ(∆p) are locally increasing and decreasing with respect to p, respectively. We show the existence of non-homological eigenvalue of ∆p, and for general eigenvalues, the local monotonicity doesn’t hold, but we have the upper semi-continuity of the spectra of graph p-Laplacians with respect to p. The k-th min-max eigenvalue λk(∆p) is a…

## One Citation

Nodal domain count for the generalized graph $p$-Laplacian

- Mathematics, Computer Science
- 2022

It is shown how to transfer Weyl’s inequalities for the Laplacian operator to the nonlinear case and prove new upper and lower bounds on the number of nodal domains of every eigenfunction of the generalized p-LaPLacian on generic graphs, including variational eigenpairs.

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