Polynomial-time algorithm for weighted efficient domination problem on diameter three planar graphs

In this paper, we update this Hasse diagram by showing that, while for every integer d such that d=3k or d=3k+2, where k≥1, the ED problem remains NP-complete for graphs of diameter d, the weighted version of the problem is solvable in time O(|V(G)|+|E(G)|) in the class of diameter three bipartite graphs and in time O(|V(G)|5) in the class of diameter three planar graphs.