Strong Domination Number of Some Graphs

In this paper, we consider strong domination number of P n k  and C n k .  Let  G=(V,E) be a graph, V is a vertex set and E is an edge set of graph G and u,v ∈V . u strongly dominates v and v weakly dominates u if  (i) uv ∈ E and (ii) d ( u, G ) ≥ d ( v, G ) . A set D ⊂V  is a strong-dominating set ( sd -set) of G if every vertex in V-D is strongly dominated by at least one vertex in D . The strong domination number γ s of G is the minimum cardinality of an sd -set.