2024/12/03 by Takumi Gomyou, Gomyou, Takumi, Shin Nayatani +1
Mathematics · #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2412.02179
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.