A note on Fiedler value of classes with sublinear separators

The n-th Fiedler value of a class of graphs C is the maximum second eigenvalue λ2(G) of a graph G∈C with n vertices. In this note we relate this value to shallow minors and, as a corollary, we determine the right order of the n-th Fiedler value for some minor closed classes of graphs, including the class of planar graphs.