Let G be a graph, and let w positive real-valued weight function on V(G). For every subset S of V(G), w(S)=?v?Sw(v). A non-empty S?V(G) is weighted safe set (G,w) if, for component C the subgraph induced by D G?S, we have w(C)?w(D) whenever there an edge between D. If connected, then called connected (G,w). The number s(G,w) cs(G,w) are minimum weights w(S) among all sets (G,w), respectively. N...