Upper eigenvalue bounds for the Kirchhoff Laplacian on embedded metric graphs

DOI10.4171/JST/388zbMath1484.35302arXiv2004.03230MaRDI QIDQ2078948

Marvin Plümer

Publication date: 4 March 2022

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.03230

zbMATH Keywords

planar graphsweighted graphsLaplacianquantum graphsspectral geometrygraph embeddings

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Linear difference operators (47B39) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (3)

Quantum trees which maximize higher eigenvalues are unbalanced ⋮ Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ On torsional rigidity and ground-state energy of compact quantum graphs

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