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.
From: Takumi Gomyou [view email]
[v1]
Tue, 3 Dec 2024 05:26:16 UTC (12 KB)
[v2]
Fri, 4 Sep 2026 14:12:37 UTC (16 KB)
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