4 papers
On the sum of the two largest eigenvalues of the curl-curl operator on graphs
Yueli Han, Lu Lu, Jianfeng Wang
The Grone--Merris conjecture, proved by Bai in~2011, states that the spectrum of the graph Laplacian is majorized by the conjugate o…
Extremal eigenvalues of combinatorial Hodge Laplacians
Zhen Chen, Suil O, Jianfeng Wang
For a finite simplicial complex on , the combinatorial Hodge Laplacian splits as , and Duval and Reiner showed that $λ_{\max}(L_k^{\…
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…