A245291 -id:A245291 - cp's OEIS frontend

A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics.

1, 31, 5119, 9961471, 259577085951, 94554701453852671, 494214691850093043122175, 37747948215762478445361018961919, 42694960288928350006693371507341885702143, 722273364120299921501331975953872089285372151857151

Offset: 1

Chai Wah Wu, Jul 16 2014

nonn

Since separability is not invariant under graph isomorphism, all 2^(n(2n-1))-1 nonzero Laplacian matrices are treated as different. A nonzero Laplacian matrix different from the complete graph is separable in C^2 X C^n if and only if its complement is. Since the complete graph is separable, this means that a(n) is odd for all n.

Chai Wah Wu, Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices, Physics Letters A, 351 (2006), 18-22.
Chai Wah Wu, Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics, arXiv:1407.5663 [quant-ph], 2014.

Cf. A245291, A229865.

a(n) + A245291(n) = 2^(n*(2*n-1))-1.

a(n) = 2^(n*(n-1))*A229865(n)-1.

cp's OEIS Frontend

A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics.

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