Problem 1886. Graceful Double Wheel Graph

Created by Richard Zapor

Solve Later

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"}]}

<a href = "http://en.wikipedia.org/wiki/Graceful_labeling">Graceful Graphs</a> are the topic of the <a href = "http://www.azspcs.net/Contest/GracefulGraphs">Primes Graceful Graph Contest</a> , 21 September 2013 thru 21 December 2013.This Challenge is to create <a href = "http://www.comp.leeds.ac.uk/bms/Graceful/doublewheel.html">Graceful Double Wheel Graphs</a> for various N. A <a href = "http://www.cs.cornell.edu/~lebras/publications/LeBras2013Double.pdf">General Algorithm by Le Bras of Cornell</a> may be helpful, Section 3 for Even/Odd Rings. The Double Wheel Graph produces valid but not Maximum Edge Graceful Graph solutions based upon <a href = "http://oeis.org/A004137">OEIS A004137</a>.Example:
One solution for N=11:<img src = "http://www.comp.leeds.ac.uk/bms/Graceful/Images/2C5+K1.gif">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 ]

<http://en.wikipedia.org/wiki/Graceful_labeling Graceful Graphs> are the topic of the <http://www.azspcs.net/Contest/GracefulGraphs Primes Graceful Graph Contest> , 21 September 2013 thru 21 December 2013.

This Challenge is to create <http://www.comp.leeds.ac.uk/bms/Graceful/doublewheel.html Graceful Double Wheel Graphs> for various N. A <http://www.cs.cornell.edu/~lebras/publications/LeBras2013Double.pdf 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 <http://oeis.org/A004137 OEIS A004137>.

*Example:*
One solution for N=11:

<<http://www.comp.leeds.ac.uk/bms/Graceful/Images/2C5+K1.gif>>

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 ]

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Problem 1886. Graceful Double Wheel Graph

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