Pair of orthogonal k-cycle decompositions of the cocktail party graph of order v = 2nk+2.
The first decomposition is given by a set B of base cycles, the second one can be obtained multiplying every cycle of B by w.
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n = 1. Base cycles of a cyclic 3-cycle decomposition of the cocktail party graph of order 8: w = -1.
[ [ 0, 1, 6 ] ]
n = 1. Base cycles of a cyclic 4-cycle decomposition of the cocktail party graph of order 10: w = -1.
[ [ 0, 1, 8, 6 ] ]
n = 2. Base cycles of a cyclic 4-cycle decomposition of the cocktail party graph of order 18: w = -1.
[ [ 0, 3, 14, 10 ],
[ 0, 1, 14, 12 ] ]
n = 3. Base cycles of a cyclic 4-cycle decomposition of the cocktail party graph of order 26: w = -1.
[ [ 0, 5, 20, 14 ],
[ 0, 3, 20, 16 ],
[ 0, 1, 20, 18 ] ]
n = 3. Base cycles of a cyclic 5-cycle decomposition of the cocktail party graph of order 32: w = -1.
[ [ 0, 4, 28, 8, 14 ],
[ 0, 5, 27, 8, 15 ],
[ 0, 1, 31, 8, 11 ] ]
n = 4. Base cycles of a cyclic 5-cycle decomposition of the cocktail party graph of order 42: w = -1.
[ [ 0, 1, 41, 17, 20 ],
[ 0, 6, 37, 9, 16 ],
[ 0, 4, 36, 11, 19 ],
[ 0, 5, 35, 6, 15 ] ]
n = 2. Base cycles of a cyclic 6-cycle decomposition of the cocktail party graph of order 26: w = 5.
[ [ 0, 1, 25, 2, 23, 19 ],
[ 0, 6, 24, 8, 23, 14 ] ]
n = 4. Base cycles of a cyclic 6-cycle decomposition of the cocktail party graph of order 50: w = 3.
[ [ 0, 1, 49, 2, 47, 43 ],
[ 0, 6, 48, 8, 47, 38 ],
[ 0, 13, 49, 14, 47, 31 ],
[ 0, 18, 48, 20, 47, 26 ] ]
n = 1. Base cycles of a cyclic 7-cycle decomposition of the cocktail party graph of order 16: w = 3.
[ [ 0, 1, 14, 2, 12, 7, 9 ] ]
n = 4. Base cycles of a cyclic 7-cycle decomposition of the cocktail party graph of order 58: w = -1.
[ [ 0, 1, 53, 14, 45, 25, 30 ],
[ 0, 2, 49, 8, 41, 23, 32 ],
[ 0, 3, 51, 8, 43, 27, 34 ],
[ 0, 4, 50, 5, 42, 28, 36 ] ]
n = 5. Base cycles of a cyclic 7-cycle decomposition of the cocktail party graph of order 72: w = -1.
[ [ 0, 1, 59, 11, 49, 24, 37 ],
[ 0, 2, 66, 16, 56, 33, 39 ],
[ 0, 3, 63, 11, 53, 32, 41 ],
[ 0, 4, 65, 11, 55, 36, 43 ],
[ 0, 5, 62, 6, 52, 35, 45 ] ]
n = 1. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 18: w = 7.
[ [ 0, 1, 16, 9, 14, 8, 12, 10 ] ]
n = 2. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 34: w = 3.
[ [ 0, 3, 30, 7, 26, 14, 22, 18 ],
[ 0, 1, 30, 5, 26, 16, 22, 20 ] ]
n = 3. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 50: w = 3.
[ [ 0, 5, 44, 11, 38, 20, 32, 26 ],
[ 0, 3, 44, 9, 38, 22, 32, 28 ],
[ 0, 1, 44, 7, 38, 24, 32, 30 ] ]
n = 4. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 66: w = 5.
[ [ 0, 7, 58, 15, 50, 26, 42, 34 ],
[ 0, 5, 58, 13, 50, 28, 42, 36 ],
[ 0, 3, 58, 11, 50, 30, 42, 38 ],
[ 0, 1, 58, 9, 50, 32, 42, 40 ] ]
n = 5. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 82: w = 3.
[ [ 0, 9, 72, 19, 62, 32, 52, 42 ],
[ 0, 7, 72, 17, 62, 34, 52, 44 ],
[ 0, 5, 72, 15, 62, 36, 52, 46 ],
[ 0, 3, 72, 13, 62, 38, 52, 48 ],
[ 0, 1, 72, 11, 62, 40, 52, 50 ] ]
n = 6. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 98: w = 3.
[ [ 0, 11, 86, 23, 74, 38, 62, 50 ],
[ 0, 9, 86, 21, 74, 40, 62, 52 ],
[ 0, 7, 86, 19, 74, 42, 62, 54 ],
[ 0, 5, 86, 17, 74, 44, 62, 56 ],
[ 0, 3, 86, 15, 74, 46, 62, 58 ],
[ 0, 1, 86, 13, 74, 48, 62, 60 ] ]
n = 7. Base cycles of a cyclic 8-cycle decomposition of the cocktail party graph of order 114: w = 5.
[ [ 0, 13, 100, 27, 86, 44, 72, 58 ],
[ 0, 11, 100, 25, 86, 46, 72, 60 ],
[ 0, 9, 100, 23, 86, 48, 72, 62 ],
[ 0, 7, 100, 21, 86, 50, 72, 64 ],
[ 0, 5, 100, 19, 86, 52, 72, 66 ],
[ 0, 3, 100, 17, 86, 54, 72, 68 ],
[ 0, 1, 100, 15, 86, 56, 72, 70 ] ]
n = 3. Base cycles of a cyclic 9-cycle decomposition of the cocktail party graph of order 56: w = 3.
[ [ 0, 4, 10, 52, 16, 46, 25, 37, 29 ],
[ 0, 5, 12, 53, 15, 47, 28, 41, 31 ],
[ 0, 1, 4, 49, 9, 43, 26, 35, 33 ] ]
n = 4. Base cycles of a cyclic 9-cycle decomposition of the cocktail party graph of order 74: w = 3.
[ [ 0, 1, 4, 58, 11, 50, 22, 40, 38 ],
[ 0, 6, 13, 71, 22, 63, 37, 51, 40 ],
[ 0, 4, 12, 67, 16, 59, 35, 52, 42 ],
[ 0, 5, 14, 73, 20, 65, 43, 56, 44 ] ]
n = 7. Base cycles of a cyclic 9-cycle decomposition of the cocktail party graph of order 128: w = -1.
[ [ 0, 9, 19, 113, 33, 99, 50, 82, 65 ],
[ 0, 7, 18, 116, 34, 102, 55, 83, 67 ],
[ 0, 8, 21, 123, 39, 109, 64, 88, 69 ],
[ 0, 5, 17, 110, 24, 96, 53, 86, 71 ],
[ 0, 6, 20, 117, 29, 103, 62, 91, 73 ],
[ 0, 4, 24, 125, 35, 111, 72, 97, 75 ],
[ 0, 1, 4, 109, 17, 95, 58, 79, 77 ] ]
n = 8. Base cycles of a cyclic 9-cycle decomposition of the cocktail party graph of order 146: w = -1.
[ [ 0, 1, 4, 110, 19, 94, 38, 76, 74 ],
[ 0, 10, 21, 131, 38, 115, 61, 95, 76 ],
[ 0, 6, 18, 132, 37, 116, 64, 94, 78 ],
[ 0, 4, 17, 135, 38, 119, 69, 95, 80 ],
[ 0, 9, 23, 130, 31, 114, 66, 103, 82 ],
[ 0, 7, 24, 135, 34, 119, 73, 106, 84 ],
[ 0, 8, 26, 141, 38, 125, 81, 110, 86 ],
[ 0, 5, 25, 144, 39, 128, 86, 111, 88 ] ]
n = 2. Base cycles of a cyclic 10-cycle decomposition of the cocktail party graph of order 42: w = 5.
[ [ 0, 1, 41, 2, 39, 12, 35, 19, 26, 22 ],
[ 0, 6, 40, 8, 39, 10, 35, 21, 33, 24 ] ]
n = 4. Base cycles of a cyclic 10-cycle decomposition of the cocktail party graph of order 82: w = 3.
[ [ 0, 1, 81, 2, 79, 28, 71, 39, 46, 42 ],
[ 0, 6, 80, 8, 79, 26, 71, 41, 53, 44 ],
[ 0, 13, 81, 14, 79, 24, 71, 43, 62, 46 ],
[ 0, 18, 80, 20, 79, 22, 71, 45, 69, 48 ] ]
n = 6. Base cycles of a cyclic 10-cycle decomposition of the cocktail party graph of order 122: w = 3.
[ [ 0, 1, 121, 2, 119, 44, 107, 59, 66, 62 ],
[ 0, 6, 120, 8, 119, 42, 107, 61, 73, 64 ],
[ 0, 13, 121, 14, 119, 40, 107, 63, 82, 66 ],
[ 0, 18, 120, 20, 119, 38, 107, 65, 89, 68 ],
[ 0, 25, 121, 26, 119, 36, 107, 67, 98, 70 ],
[ 0, 30, 120, 32, 119, 34, 107, 69, 105, 72 ] ]
n = 8. Base cycles of a cyclic 10-cycle decomposition of the cocktail party graph of order 162: w = 7.
[ [ 0, 1, 161, 2, 159, 60, 143, 79, 86, 82 ],
[ 0, 6, 160, 8, 159, 58, 143, 81, 93, 84 ],
[ 0, 13, 161, 14, 159, 56, 143, 83, 102, 86 ],
[ 0, 18, 160, 20, 159, 54, 143, 85, 109, 88 ],
[ 0, 25, 161, 26, 159, 52, 143, 87, 118, 90 ],
[ 0, 30, 160, 32, 159, 50, 143, 89, 125, 92 ],
[ 0, 37, 161, 38, 159, 48, 143, 91, 134, 94 ],
[ 0, 42, 160, 44, 159, 46, 143, 93, 141, 96 ] ]