Maximization of the first Laplace eigenvalue of a finite graph II

Takumi Gomyou, Shin Nayatani

Published 2024-12-03Version 1

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.