Characterizations of Trees With Equal Paired and Double Domination Numbers
A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, and a double dominating set is a dominating set that dominates every vertex of G at least twice. We show that for trees, the paired-domination number is less than or equal to the double domination number, solving a conjecture of Chellali and Haynes. Then we characterize the trees having equal paired and double domination numbers.
Blidia, Mostafa; Chellali, Mustapha; and Haynes, Teresa W.. 2006. Characterizations of Trees With Equal Paired and Double Domination Numbers. Discrete Mathematics. Vol.306(16). 1840-1845. https://doi.org/10.1016/j.disc.2006.03.061 ISSN: 0012-365X