The cofactor of R[S] equals (-2)^{|S|-1} κ_G(S)/τ(G), and the normalized det R[S]/cof R[S] equals (2/|S|) tr Q + (1/2) q^T K q after Kron reduction, equivalently the max of u^T R[S] u for sum-u=1 vectors.
Resistance distance
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
Middle-mile logistics is cast as a multi-object goal-conditioned MDP and solved by combining graph neural networks with model-free RL via extraction of small feature graphs.
Self-organising memristive networks exhibit collective nonlinear dynamics that can support physical learning with parallels to biological plasticity and potential for energy-efficient edge intelligence.
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Principal minors of effective-resistance matrices and local resistance radii
The cofactor of R[S] equals (-2)^{|S|-1} κ_G(S)/τ(G), and the normalized det R[S]/cof R[S] equals (2/|S|) tr Q + (1/2) q^T K q after Kron reduction, equivalently the max of u^T R[S] u for sum-u=1 vectors.
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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.