2. Second Eigenvalue Multiplicity
Let G be a graph with maximum degree bounded by \Delta. The maximum possible multiplicity of the second eigenvalue of various matrices associated with the graph is of interest. For the following choices of Hermitian matrix M_G associated with G, what is the maximum multiplicity of the second largest eigenvalue of M_G?Cite this as: AimPL: Spectral graph and hypergraph theory: connections and applications, available at http://aimpl.org/spectralhypergraph.