• Corpus ID: 244488736

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… 

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