Extremal copositive matrices with minimal zero supports of cardinality two

Abstract

Let $A \in {\cal C}^n$ be an extremal copositive matrix with unit diagonal. Then the minimal zeros of $A$ all have supports of cardinality two if and only if the elements of $A$ are all from the set $\{-1,0,1\}$. Thus the extremal copositive matrices with minimal zero supports of cardinality two are exactly those matrices which can be obtained by diagonal scaling from the extremal $\{-1,0,1\}$ unit diagonal matrices characterized by Hoffman and Pereira in 1973.