Extremal rays and duals for cones of positive definite matrices with prescribed zeros

Given an undirected graph G with vertices 1, … , n consider the cone PG of the (n, n) real positive definite matrices y =(yij) such that yij = 0 if {i, j} is not an edge. The present paper computes the dual of PG and the extremal rays of the closure when G is a decomposable graph and when G is the four cycle graph.