2003/12/15 by Tuerker Biyikoglu, Biyikoglu, Tuerker, Josef Leydold +1 · 1 citation
Mathematics · #05C05 #05C35 #05C50 #05C75 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Point processes and geometric inequalities #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CO #math.SP #msc:05C05 #msc:05C35 #msc:05C50 #msc:05C75
paper · pdf · doi:10.48550/arxiv.math/0312287
19 pages, 5 figures
arxiv created 2003/12/15 · openalex publication_date 2003/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Faber-Krahn theorem states that among all bounded domains with the same volume in \mathbb 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.