4 papers
Krahn--SzegÅ type inequalities and nodal domain methods on graphs
Huiqiu Lin, Lianping Liu, Xilong Yin +1
We study discrete analogues of classical spectral geometric inequalities and extremal eigenvalue problems on graphs. The classical Krahn--SzegÅ inequality states that, among bound…
A Faber--Krahn inequality for trees
Huiqiu Lin, Lianping Liu, Zhe You
The well-known Faber-Krahn theorem states that the ball has the lowest first Dirichlet eigenvalue among all domains of the same volume in . Leydold (Geom. Funct. Anal…
Estimates of the first Dirichlet eigenvalue of graphs
Huiqiu Lin, Lianping Liu, Zhe You +1
Inspired by the Li--Yau eigenvalue-diameter estimates, we investigate lower bounds for the first Dirichlet eigenvalue in terms of the diameter (or inscribed radius) of a graph. Let…
Upper bounds of Steklov eigenvalues on graphs
Huiqiu Lin, Lianping Liu, Zhe You +1
Let and be the maximum vertex degree and a subset of vertices in a graph respectively. In this paper, we study the first (non-trivial) Steklov eigenvalue of …