Optimal -locating–dominating codes in the infinite king grid.

Abstract: Assume that is an undirected graph with vertex set and edge set . The ball denotes the vertices within graphical distance from . A subset is called an -locating–dominating code of type B if the sets are distinct for all subsets with at most vertices. We give examples of optimal -locating–dominating codes of type in the infinite king grid for all and prove optimality. The infinite king grid is the graph with vertex set and edge set . [Copyright &y& Elsevier]