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math.SP2023
New graph invariants based on -Laplacian eigenvalues
Chuanyuan Ge, Shiping Liu, Dong Zhang
We present monotonicity inequalities for certain functions involving eigenvalues of -Laplacians on signed graphs with respect to . Inspired by such monotonicity, we propose n…
math.SP2022
Nodal domain theorems for -Laplacians on signed graphs
Chuanyuan Ge, Shiping Liu, Dong Zhang
We establish various nodal domain theorems for -Laplacians on signed graphs, which unify most of the existing results on nodal domains of graph -Laplacians and arbitrary symm…
math.SP2022
Symmetric Matrices, Signed Graphs, and Nodal Domain Theorems
Chuanyuan Ge, Shiping Liu
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunctions of generalized Laplacians, i.e., symmetric matrices with non-positive off-d…