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arXiv · 2412.02179

Maximization of the first Laplace eigenvalue of a finite graph II

Takumi Gomyou·Shin Nayatani
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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 finite if and only if the graph is a tree. We also prove that the supremum of the first nonzero eigenvalue is nonincreasing under taking a subgraph.

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Takumi Gomyou, Shin Nayatani. 2026-09-04. Maximization of the first Laplace eigenvalue of a finite graph II. https://arxiv.org/abs/2412.02179

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