Exactly fourteen intrinsically knotted graphs have 21 edges
  Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by rY moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges. 
Min Jung Lee, Hyoung Jun Kim, Hwa Jeong Lee, and Seungsang Oh
math.GT