THE TRIANGLE GRAPH T-6 IS NOT SPN

A real symmetric matrix A is copositive if x' Ax >= 0 for every nonnegative vector x. A matrix is SPN if it is a sum of a real positive semidefinite matrix and a nonnegative matrix. Every SPN matrix is copositive, but the converse does not hold for matrices of order greater than 4. A graph G is an SPN graph if every copositive matrix whose graph is G is SPN. It is shown that the triangle graph T-6 is not SPN.