A perfect ruler also called a complete ruler, is type of ruler considered by Guy (1994) which has 
distinct marks spaced such that the distances between marks
can be used to measure all the distances 1, 2, 3, 4, ... up to some maximum distance
. Such a ruler can be constructed
from a perfect difference set by subtracting
one from each element. For example, the perfect
difference set 
gives 0, 1, 4, 6, which can be used to measure 
, 
, 
, 
, 
, 
(so we get 6 distances with only four marks).
Perfect rulers can be used to generate graceful graphs.
