A Linear Time Algorithm for Weighted k-Fair Domination Problem in Cactus Graphs

A set D of vertices in a graph G is k-fair dominating if every vertex not adjacent to exactly k D. The weighted domination number $$\mathrm {wfd}_k(G)$$ vertex-weighted the minimum weight w(D) among all sets In addition number, some auxiliary parameters are defined. It shown that for cactus graph, and can be calculated linear time.