A graph discretization of vector Laplace operator

2023/12/10 by Li, Shu, Lu, Lu, Wang, Jianfeng
#05C50 #35J05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.05754

Abstract

In this paper, we study the graph-theoretic analogues of vector Laplacian (or Helmholtz operator) and vector Laplace equation. We determine the graph matrix representation of vector Laplacian and obtain the dimension of solution space of vector Laplace equation on graphs.

Related

• A graph discretization of the Laplace-Beltrami operator
• Calculus on Graphs
• A survey of graph laplacians
• Graph approximations to the Laplacian spectra
• Graph Laplacians with Higher Accuracy