Minimal CP rank

For every completely positive matrix A, cp-rankA ≥ rankA. Let cp-rankG be the maximal cp-rank of a CP matrix realization of G. Then for every graph G on n vertices, cp-rankG ≥ n. In this paper the graphs G on n vertices for which equality holds in the last inequality, and graphs G such that cp-rankA = rankA for every CP matrix realization A of G, are… (More)