Minimal graphs with disjoint dominating and total dominating sets

Abstract

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 provide a characterization of DTDP-graphs, where here we allow multi-edges and multi-loops.