  Let G be a graph with adjacency matrix A(G). Consider the matrix IA(G)=(I |
A(G)), where I is the identity matrix, and let M(IA(G)) be the binary matroid
represented by IA(G). Then suitably parametrized versions of the Tutte
polynomial of M(IA(G)) yield the interlace polynomials of G, introduced by
Arratia, Bollob\'as and Sorkin [J. Combin. Theory Ser. B 92 (2004) 199-233;
Combinatorica 24 (2004) 567-584]. Interlace polynomials subsequently introduced
by other authors may be obtained from parametrized Tutte polynomials of the
binary matroid represented by (I | A(G) | I+A(G)).
