- Graph invariants in the spin model
- Journal of Combinatorial Theory Series B
- Volume | Issue number
- 99 | 2
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
- Given a symmetric n x n matrix A, we define, for any graph G,
f(A)(G) := Sigma(phi:VG ->[1,...,n]) Pi(uv is an element of EG) a(phi(u),phi(v).)
We characterize for which graph parameters f there is a complex matrix A with f = f(A), and similarly for real A. We show that f(A) uniquely determines A, up to permuting rows and (simultaneously) columns. The proofs are based on the Nullstellensatz and some elementary invariant-theoretic techniques.
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