A subdifferential framework certifies conformal rigidity via orbit-isometric embeddings, reducing the problem for vertex-transitive graphs to a single-eigenvector check and in general to linear feasibility or Gröbner bases.
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A graph is totally conformally rigid if and only if it is edge-rigid (every canonical spectral embedding onto a Laplacian eigenspace is edge-isometric), which is equivalent to all edges being pairwise Laplacian-cospectral, enabling a polynomial-time decision algorithm via SDP duality.
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Conformal Rigidity of Graphs: Subdifferentials and Orbit-Isometries
A subdifferential framework certifies conformal rigidity via orbit-isometric embeddings, reducing the problem for vertex-transitive graphs to a single-eigenvector check and in general to linear feasibility or Gröbner bases.
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Total Conformal Rigidity in Graphs
A graph is totally conformally rigid if and only if it is edge-rigid (every canonical spectral embedding onto a Laplacian eigenspace is edge-isometric), which is equivalent to all edges being pairwise Laplacian-cospectral, enabling a polynomial-time decision algorithm via SDP duality.