  A graph $G$ is a DTDP-graph if it has a pair $(D,T)$ of disjoint sets of
vertices of $G$ such that $D$ is a dominating set and $T$ is a total dominating
set of $G$. Such graphs were studied in a number of research papers. In this
paper we study further properties of DTDP-graphs and, in particular, we
characterize minimal DTDP-gaphs without loops.
