ELA, Volume 8, pp. 140-157, December 2001, abstract.

Minimal CP rank

Naomi Shaked-Monderer

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 characterized.