The inertia sets of graphs with a 2-separation

For a graph G=(V,E) with V={1,2,…,n}, let S(G) be the set of all symmetric real n×n matrices A=[ai,j] with ai,j≠0, i≠j if and only if ij∈E. The inertia set of a graph G is the set of all possible inertias of matrices in S(G). In this paper we give a formula that expresses the inertia set of a graph with a 2-separation in terms of the inertia sets of subgraphs of G. This formula follows from an extension to arbitrary fields with characteristic not equal to two.