Quantum graphs which optimize the spectral gap (Q1675054)

The paper under review deals with quantum graphs; that is, a metric graph with the Laplacian with Kirchhoff coupling condition on it. The authors study the first positive eigenvalue (i.e. the spectral gap) and investigate supremizers and infimizers of graph topologies for the spectral gap, given a fixed total edge length of the graph. Special situations thes consider are graphs with (and without) a bridge, tree graphs with leaves, as well as simplicity of the first positive eigenvalue.