Exact double domination in graphs

Mustapha Chellali, Abdelkader Khelladi, Frédéric Maffray
2005 Discussiones Mathematicae Graph Theory  
In a graph a vertex is said to dominate itself and all its neighbours. A doubly dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. A doubly dominating set is exact if every vertex of G is dominated exactly twice. We prove that the existence of an exact doubly dominating set is an NP-complete problem. We show that if an exact double dominating set exists then all such sets have the same size, and we establish bounds on this size. We give a
more » ... e. We give a constructive characterization of those trees that admit a doubly dominating set, and we establish a necessary and sufficient condition for the existence of an exact doubly dominating set in a connected cubic graph.
doi:10.7151/dmgt.1282 fatcat:wbnrrfu6d5ep5c3wuw2as3epvm