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For every completely positive matrix A, cp-rank A ≥ rank A. Let cp-rank G be the maximal cp-rank of a CP matrix realization of G. Then for every graph G on n vertices, cp-rank G ≥ n. In this paper the graphs G on n vertices for which equality holds in the last inequality, and graphs G such that cp-rank A = rank A for every CP matrix realization A of G, are characterized.doi:10.13001/1081-3810.1067 fatcat:js4cfi2whbh4jp3kigees562za