Hyper Domination in Bipartite Semigraphs

Let S be a bipartite semigraph with |NXa(y)| ≥ 1 for every y ∈ Y . A vertex x ∈ X hyper dominates y ∈ Y if y ∈ Na(x) or y ∈ Na(NY a(x)). A subsetD ⊆ X is a hyper dominating set of S if every y ∈ Y is hyper dominated by a vertex ofD. A subsetD ⊆ X is called a minimal hyper dominating set of S if no proper subset of D is a hyper dominating set of S. The minimum cardinality of a minimal hyper dominating set of S is called hyper domination number of S and is denoted by γha(S). The concept of hyper independence and hyper irredundant is introduced. Inequalities involving dominating parameters and irredundant parameters are proved. Key–Words: Semigraphs, Bipartite semigraphs, hyper dominating set, hyper independent set, hyper irredundant set.