Graceful Graphs are the topic of the Primes Graceful Graph Contest , 21 September 2013 thru 21 December 2013.

This Challenge is to create Graceful Double Wheel Graphs for various N. A General Algorithm by Le Bras of Cornell may be helpful, Section 3 for Even/Odd Rings. The Double Wheel Graph produces valid but not Maximum Edge Graceful Graph solutions based upon OEIS A004137.

Example: One solution for N=11:

which could be answered as [1 3 14 6 19;20 5 17 7 16].

There are 20 links and thus the absolute differences between connected nodes must produce values 1 thru 20. The max node value is equal to the number of links and the min is zero, at the center of the Double Wheel.

Input: N [Total number of Nodes (odd) and N>10 ]

Output: M [ Matrix size [(N-1)/2, 2] of node values where row-1 is outer and row-2 is inner ring ]