The switching class of A_A(G) = D^T D - 2I determines G modulo isolates, and its frustration index equals 1/4 sum d(v)^2 minus 1/4 the maximum ||Dx||^2 over sign vectors x on edges, yielding spectral bounds on bipartization.
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The Antisymmetric Line Graph
The switching class of A_A(G) = D^T D - 2I determines G modulo isolates, and its frustration index equals 1/4 sum d(v)^2 minus 1/4 the maximum ||Dx||^2 over sign vectors x on edges, yielding spectral bounds on bipartization.