The maximum corank of graphs with a 2-separation

For a graph G=(V,E) with vertex-set V={1,2,…,n}, which is allowed to have parallel edges, and for a field F, let S(G;F) be the set of all F-valued symmetric n×n matrices A which represent G. The maximum corank of a graph G is the maximum possible corank over all A∈S(G;F). If (G1,G2) is a (⩽2)-separation, we give a formula which relates the maximum corank of G to the maximum corank of some small variations of G1 and G2.