Shuffle-Exchange Graph

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length  binary strings with an edge from  to  if

1.  differs from  in its last bit, or

2.  is obtained from  by a left or right cyclic shift.

The -dimensional shuffle-exchange graph is implemented as ShuffleExchangeGraph[n] in the Wolfram Language package Combinatorica` .

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.