Minimal CP rank
Naomi Shaked-Monderer · Electronic Journal of Linear Algebra · 2001
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 =r ankA for every CP matrix realization A of G ,a re characterized.