Binary matroids and local complementation

We introduce a binary matroid M[IAS(G)]M[IAS(G)] associated with a looped simple graph GG. M[IAS(G)]M[IAS(G)] classifies GG up to local equivalence, and determines the delta-matroid and isotropic system associated with GG. Moreover, a parametrized form of its Tutte polynomial yields the interlace polynomials of GG.