A note on a relation between the weak and strong domination numbers of a graph
Razika Boutrig, Mustapha Chellali · Opuscula Mathematica · 2012
In a graph G = (V, E) a vertex is said to dominate itself and all its neighbors., respectively).The weak (strong, respectively) domination number of G, denoted by γw(G) (γs(G), respectively), is the minimum cardinality of a weak (strong, respectively) dominating set of G.In this note we show that if G is a connected graph of order n ≥ 3, then γw(G) + tγs(G) ≤ n, where t = 3/(∆ + 1) if G is an arbitrary graph, t = 3/5 if G is a block graph, and t = 2/3 if G is a claw free graph.