Domatically perfect graphs
Naoki Matsumoto · AKCE International Journal of Graphs and Combinatorics · 2019
A graph G of order n is domatically perfect if d(G)=n∕γ(G), where γ(G) and d(G) denote the domination number and the domatic number, respectively. In this paper, we give basic results for domatically perfect graphs, and study a main problem; for a given graph G, to find a necessary and sufficient condition for G and its complement to be both domatically perfect. Moreover, we investigate domatically complete graphs, which are domatically full and domatically perfect.