Two empty graphs:
( )

Two singleton graphs:
( 0 )

Empty and singleton graphs:

Two rings:
( 0 1 2 3 4 )
( 0 4 3 2 1 )
( 1 0 4 3 2 )
( 1 2 3 4 0 )
( 2 1 0 4 3 )
( 2 3 4 0 1 )
( 3 2 1 0 4 )
( 3 4 0 1 2 )
( 4 0 1 2 3 )
( 4 3 2 1 0 )

Two directed rings:
( 0 1 2 3 4 )
( 1 2 3 4 0 )
( 2 3 4 0 1 )
( 3 4 0 1 2 )
( 4 0 1 2 3 )

Two rings where node parity should be equal:
( 0 1 2 3 4 )
( 4 3 2 1 0 )

Two rings where edge parity should be equal:
( 0 1 2 3 4 )
( 0 4 3 2 1 )

Two rings with only one vertex coloring:
( 0 1 2 3 4 )
( 0 4 3 2 1 )
( 1 0 4 3 2 )
( 1 2 3 4 0 )
( 2 1 0 4 3 )
( 2 3 4 0 1 )
( 3 2 1 0 4 )
( 3 4 0 1 2 )
( 4 0 1 2 3 )
( 4 3 2 1 0 )

Two rings with vertex coloring:
( 0 1 2 3 4 )
( 4 3 2 1 0 )

Two rings with edge coloring:
( 0 1 2 3 4 )
( 0 4 3 2 1 )

Two rings where node of graph 1 should not be 3 higher than node of graph 2:
( 0 1 2 3 4 )
( 1 0 4 3 2 )
( 1 2 3 4 0 )
( 2 1 0 4 3 )
( 2 3 4 0 1 )
( 4 0 1 2 3 )
( 4 3 2 1 0 )

Two rings with different directedness.