The Fiedler value λ2, also known as algebraic connectivity, is the
second smallest Laplacian eigenvalue of a graph. We study the maximum Fiedler
value among all planar graphs G with n vertices, denoted by
λ2max, and we show the bounds 2+Θ(n21)≤λ2max≤2+O(n1). We also provide bounds on the maximum
Fiedler value for the following classes of planar graphs: Bipartite planar
graphs, bipartite planar graphs with minimum vertex degree~3, and outerplanar
graphs. Furthermore, we derive almost tight bounds on λ2max for two
more classes of graphs, those of bounded genus and Kh-minor-free graphs.Comment: 21 pages, 4 figures, 1 table. Version accepted in Linear Algebra and
Its Application