The Domination Parameters of Cubic Graphs

Let ir(G), γ(G), i(G), β0(G), Γ(G) and IR(G) be the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number of a graph G, respectively. In this paper we show that for any integers k1, k2, k3, k4, k5 there exists a cubic graph G satisfying the following conditions: γ(G)−ir(G) ≥ k1, i(G)−γ(G) ≥ k2, β0(G) − i(G) ≥ k3, Γ(G) − β0(G) ≥ k4, and IR(G) − Γ(G) ≥ k5. This result settles a problem posed in [8].