  For a graph $G = (V,E),$ a subset $S$ of $V$ is a perfect dominating set of
$G$ if every vertex not in $S$ is adjacent to exactly one vertex in $S.$ The
perfect domination number, $\gamma_p(G),$ is the minimum cardinality of a
perfect dominating set of $G.$ The perfect domination number is found for
knights graphs on square, rectangular, and infinite chessboards. Indeed, exact
values or bounds are given for all chessboards except those with 3 rows and
number of columns congruent to 1, 2, or 3 modulo 8.
