Cospectrality preserving graph modifications and eigenvector properties via walk equivalence of vertices

DOI10.1016/j.laa.2021.04.004zbMath1465.05104arXiv2007.07609OpenAlexW3042298036MaRDI QIDQ2029821

C. V. Morfonios, P. Schmelcher, M. Pyzh, M. Röntgen

Publication date: 4 June 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.07609

zbMATH Keywords

cospectralitysymmetric matricesmatrix powersstructure of eigenvectorswalk equivalence

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Symmetry breaking in quantum theory (81R40) Molecular physics (81V55) Signed and weighted graphs (05C22)

Related Items (1)

Isospectral reductions and quantum walks on graphs

Cites Work

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• Constructing cospectral graphs
• Controllable subsets in graphs
• General equitable decompositions for graphs with symmetries
• Unlocking the walk matrix of a graph
• Hidden symmetries in real and theoretical networks
• Characterizing cospectral vertices via isospectral reduction
• Pretty good quantum state transfer in asymmetric graphs via potential
• Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation
• Uncertainty Principles and Sparse Eigenvectors of Graphs
• How to suppress dark states in quantum networks and bio-engineered structures
• A classical approach to the graph isomorphism problem using quantum walks

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