Faber-Krahn Type Inequalities for Trees
The Faber-Krahn theorem states that among all bounded
domains with the same volume in Rn (with the standard
Euclidean metric), a ball that has lowest first Dirichlet eigenvalue.
Recently it has been shown that a similar result holds for
(semi-)regular trees. In this article we show that such a theorem
also hold for other classes of (not necessarily non-regular) trees.
However, for these new results no couterparts in the world
of the Laplace-Beltrami-operator on manifolds are known.
Mathematics Subject Classification:
*05C35 Extremal problems (graph theory),
05C75 structural characterization of types of graphs,
05C50 graphs and matrices
graph Laplacian, Dirichlet eigenvalue problem,
Faber-Krahn type inequality, tree, degree sequence