A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length 
binary strings with a directed
edge from 
to 
if
1. 
differs from 
in its last bit, or
2. 
is obtained from 
by a left or right cyclic shift.
For 
,
2, ..., the shuffle exchange graphs with self-loops removed
are isomorphic to 
, 
, 
, ..., where 
is a path graph and 
denotes the 
th 
-vertex graph in the ordering of McKay.
