7 papers
Bipartite graphs, random graphs, and Lin--Lu--Yau curvature
Huiqiu Lin, Zhe You, Da Zhao
Let be a bipartite graph with parts and where and . We show that every bipartite graph with more than edges has positive Lin--L…
Krahn--Szegő 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--Szegő inequality states that, among bounde…
Comparison between the first Steklov eigenvalue and algebraic connectivity on trees
Huiqiu Lin, Da Zhao
Trees can be regarded as discrete analogue of Hadamard manifolds, namely simply-connected Riemannian manifolds of non-positive sectional curvature. In this paper, we compare the fi…
Maximize the Steklov eigenvalue of trees
Huiqiu Lin, Da Zhao
We study the maximal Steklov eigenvalues of trees with given number of boundary vertices and total number of vertices. Trees can be regarded as discrete analogue of Hadamard manifo…
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 w…
Proof of Lew's conjecture on the spectral gaps of simplicial complexes
Xiongfeng Zhan, Xueyi Huang, Huiqiu Lin
As a generalization of graph Laplacians to higher dimensions, the combinatorial Laplacians of simplicial complexes have garnered increasing attention. Let be a simplicial compl…
The first Steklov eigenvalue of planar graphs and beyond
Huiqiu Lin, Da Zhao
The Steklov eigenvalue problem was introduced over a century ago, and its discrete form attracted interest recently. Let and be the maximum vertex degree and the set of ve…