6 papers
Generic properties of discrete Steklov eigenfunctions
Lixiang Chen, Bobo Hua, Yongtang Shi
Let be a finite connected graph with boundary . We prove that for a generic positive edge weight function , the Steklov eigenvalues of $(G,B,w)…
Helmholzian Spectra of Graphs: Novel Properties
Lu Lu, Yongtang Shi, Zoran StaniÄ +2
Let $\grad$, $\curl$, and $\dv$ be the graph-theoretic analogues of the gradient, curl, and divergence operators from multivariate calculus. The graph Laplacian $-\dv \grad$ gives…
Helmholzian spectra of graphs: basic properties
Lu Lu, Yongtang Shi, Zoran StaniÄ +2
The Helmholtzian matrix of a graph is a graph-theoretic analogue of the vector Laplacian (or Helmholtz operator) [S. Li, L. Lu, J.F. Wang, A graph discretization of…
Maximizing the Steklov eigenvalues on trees with a diameter constraint
Jiangdong Ai, Huiqiu Lin, Yongtang Shi
We study the first nonzero Steklov eigenvalue of the Dirichlet-to-Neumann operator on a finite tree with leaf boundary , under a constraint on the diameter…
The first Steklov eigenvalue bound for graphs of positive genus
Lixiang Chen, Yongtang Shi, Liwen Zhang
Let be a graph of genus with boundary . For , Lin and Zhao [J. Lond. Math. Soc. 112 (2025), Paper No. e70238] proved an upper bound for the first (non-trivial) S…
On the second-largest modulus among the eigenvalues of a power hypergraph
Changjiang Bu, Lixiang Chen, Yongtang Shi
It is well known that the algebraic multiplicity of an eigenvalue of a graph (or real symmetric matrix) is equal to the dimension of its corresponding linear eigen-subspace, also k…