Article Dans Une Revue Discrete Applied Mathematics Année : 2026

A graph discretization of vector Laplacian

Résumé

As known, the scalar Laplacian gives the celebrated Laplacian matrix of a graph. In this paper, we determine the graph matrix presentation of vector Laplacian (or Helmholtz operator), named as Helmholtzian matrix. To compare the difference and similarity with previous graph matrices, we study the limit points of spectral radius and characterize the connected graphs with spectral radius at most 4.38+ via Helmholtzian matrix. Finally, we discuss the potential applications of Helmholtzian spectra of graphs in the simplicial networks and small-world networks.

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Dates et versions

hal-05290395 , version 1 (30-09-2025)

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Shu Li, Lu Lu, Jianfeng Wang. A graph discretization of vector Laplacian. Discrete Applied Mathematics, 2026, 379, pp.446-460. ⟨10.1016/j.dam.2025.09.019⟩. ⟨hal-05290395⟩

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