Expanding and forwarding

Expanding parameters of graphs (magnification constant, edge and vertex cutset expansion) are related by very simple inequalities to forwarding parameters (edge and vertex forwarding indices). This shows that certain graphs have eccentricity close to the diameter. Connections between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of the graph are made. Graphs with unknown spectrum (de Bruijn, Kautz) are shown to be reasonable expanding by purely combinatorial arguments. Conversely, near-optimal routings in these graphs yield tight bounds on the spectrum.