Restrained Double Domination Number of a Graph
R. Kala, T. R. Nirmala Vasantha, S. Arumugam · AKCE International Journal of Graphs and Combinatorics · 2008
As etS ⊆ V (G) is a restrained double dominating set for G if every vertex in V is dominated by at least two vertices in S andV − Shas no isolated vertices. The minimum cardinality of a minimal restrained double dominating set is the restrained double domination number and is denoted by γ2r(G). In this paper we initiate a study of this parameter and obtain some bounds for γ2r(G) and characterize the graphs attaining these bounds. We also derive Nordhaus-Gaddum type results for γ2r(G).