“…Minimum weight dominating set problem (MWDS) on undirected graphs is a widely-studied problem, and many approaches (Albuquerque and Vidal, 2018;Lin and Guan, 2018;Wang et al, 2018;Lin et al, 2016;Chaurasia and Singh, 2015a;Nitash and Singh, 2014;Potluri and Singh, 2013;Jovanovic et al, 2010;Shetgaonkar and Singh, 2020) have been proposed in the literature for this problem. However, the corresponding problem in directed graphs, viz.…”