Which graphs generate irreducible copositive matrices?

A research to which graphs generate irreducible copositive matrices. This research will continue preliminary work by Peter J.C. Dickinson [1] and the goal of it is to find graphs that produce irreducible matrices. First all graphs of a small amount of vertices that produce irreducible matrices will be researched, then ways to combine graphs producing irreducible matrices to make bigger graphs producing irreducible matrices will be elaborated. Furthermore, the amount of graphs producing irreducible matrices with v(G) ≤ 13 will be discussed.