The influence of a vertex set S ⊆V(G) is I(S) = Σv∈S(1 + deg(v)) = Σv∈S |N[v]|, which is the total amount of domination done by the vertices in S. The efficient domination number F(G) of a graph G is equal to the maximum influence of a packing, that is, F(G) is the maximum number of vertices one can dominate under the restriction that no vertex gets dominated more than once.
In this paper, we consider the efficient domination number of some finite and infinite knights chessboard graphs.
Sinko A, Slater PJ. 2006. Efficient domination in knights graphs. AKCE International Journal of Graphs and Combinatorics 3(2): 193-204.