Efficient domination in knights graphs (Q2370394)

For graphs defined by the moves of a knight on finite and infinite rectangular boards the authors study the maximum cardinality of the closed neighborhood of a set of vertices of pairwise distance at least three. They characterize for which finite boards this value equals the order of the graph and which appropriately defined percentage of all vertices can be in such a closed neighborhood for various infinite boards and finite boards. In all these cases essentially nine tenth of all vertices can be covered.