The domination parameters of cubic graphs
IE Zverovich, VE Zverovich - Graphs and Combinatorics, 2005 - Springer
IE Zverovich, VE Zverovich
Graphs and Combinatorics, 2005•SpringerAbstract Let ir (G), γ (G), i (G), β 0 (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 nonnegative integers k 1, k 2, k 3, k 4, k 5 there exists a cubic
graph G satisfying the following conditions: γ (G)–ir (G)≥ k 1, i (G)–γ (G)≥ k 2, β 0 (G)–i (G)>
k 3, Γ (G)–β 0 (G)–k 4, and IR (G)–Γ (G)–k 5. This result settles a problem posed in [9].
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 nonnegative integers k 1, k 2, k 3, k 4, k 5 there exists a cubic
graph G satisfying the following conditions: γ (G)–ir (G)≥ k 1, i (G)–γ (G)≥ k 2, β 0 (G)–i (G)>
k 3, Γ (G)–β 0 (G)–k 4, and IR (G)–Γ (G)–k 5. This result settles a problem posed in [9].
Abstract
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 nonnegative 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 [9].
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