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Maximization of the first Laplace eigenvalue of a finite graph II

Combinatorics 2024-12-04 v1

Abstract

Given a length function on the set of edges of a finite graph, the corresponding Fujiwara Laplacian is defined. We consider a problem of maximizing the first nonzero eigenvalue of this graph Laplacian over all choices of edge-length function subject to a certain normalization. In this paper we prove that the supremum of the first nonzero eigenvalue is infinite whenever the graph contains a cycle.

Cite

@article{arxiv.2412.02179,
  title  = {Maximization of the first Laplace eigenvalue of a finite graph II},
  author = {Takumi Gomyou and Shin Nayatani},
  journal= {arXiv preprint arXiv:2412.02179},
  year   = {2024}
}

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12 pages