Concepts Arising from Strong Efficient Domination Number. Part – III

Let G = (V, E) be a simple graph. A subset S of V(G) is called a strong (weak) efficient dominating set of G if for every v ∈ V(G), |N_s[] ∩ S|=1. (|N_w [] ∩ S|=1), where N_s () = {u ∈V(G) : uv ∈ E(G), deg u ≥ deg v}. (N_w () = {u ∈V(G) : uv ∈ E(G), deg v ≥ deg u}). The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and is denoted by γ_se(G) (γ_we(G)). A graph G is strong efficient if there exists a strong efficient dominating set of G. The strong efficient co-bondage number (G) is the maximum cardinality of all sets of edges X ⊆ E such that γ_se( + ) ≤ γ_se(G). In this paper, further results on strong efficient co-bondage number of some special graphs are determined