Do whatever you like to try and beat the performance of algorithms 1 and 2. If you discover a smaller dominating set than the minimum known for one of the open problems, be sure to let me know.
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C80 fullerenes: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 80 : 20 22 29 20- 22 20- 22 20- 26 20- 25 22 22 30 20- 22 22 34+ 24 20- 2 80 : 20 22 31 20- 23 20- 23 20- 25 20- 25 22 22 32 20- 23 25 36+ --- 20- 3 80 : 20 22 32 20- 22 20- 22 20- 25 20- 25 23 22 29 20- 22 25 34+ --- 20- 4 80 : 20 22 31 20- 22 20- 22 20- 24 20- 25 22 22 29 20- 22 25 34+ --- 20- 5 80 : 20 23 31 20- 22 20- 22 20- 24 20- 25 22 21 25 20- 22 24 35+ --- 20- 6 80 : 20 22 31 20- 22 20- 23 20- 25 20- 25 22 22 27 20- 22 26 33+ --- 20- 7 80 : 20 22 30 20- 22 20- 22 20- 24 20- 25 22 22 24 20- 22 25 34+ --- 20- 8 80 : 20 22 31 20- 22 20- 22 20- 25 35+ 25 22 22 27 20- 22 25 34 --- 20- 9 80 : 20 22 29 20- 23 20- 23 20- 25 40+ 23 22 22 29 20- 22 24 33 --- 20- 10 80 : 20 22 31 20- 23 20- 22 20- 26 36+ 25 22 22 28 20- 22 26 34 --- 20- 11 80 : 20 22 29 20- 22 20- 20- 20- 25 20- 25 22 21 29 20- 22 24 34+ --- 20- 12 80 : 21 22 26 21- 23 22 22 21- 26 21- 25 23 22 27 21- 22 24 36+ --- 21- 13 80 : 21 22 27 21- 23 21- 22 21- 27 21- 25 23 22 --- 21- 23 25 36+ --- 21- 14 80 : 21 22 29 21- 23 21- 23 21- 25 21- 24 22 22 --- 22 22 24 35+ --- 21- 15 80 : 21 22 27 21- 23 21- 23 21- 26 21- 24 23 22 --- 21- 22 24 35+ --- 21- 16 80 : 21 22 30 21- 23 21- 22 21- 25 21- 23 22 22 --- 22 22 26 35+ --- 21- 17 80 : 21 22 30 21- 23 21- 23 21- 25 21- 24 22 21- --- 22 22 25 35+ --- 21- 18 80 : 21 22 31 21- 23 21- 23 21- 25 21- 23 22 22 --- 22 22 24 35+ --- 21- 19 80 : 21 22 28 21- 23 21- 24 21- 26 21- 23 22 22 --- 21- 22 25 35+ --- 21- 20 80 : 21 22 29 21- 23 21- 23 21- 26 21- 23 22 22 --- 21- 22 25 35+ --- 21- 21 80 : 21 23 30 21- 23 21- 23 21- 27 21- 24 23 22 --- 21- 23 26 35+ --- 21- 22 80 : 21 22 29 21- 23 21- 22 21- 26 21- 22 22 22 --- 22 22 25 35+ --- 21- 23 80 : 22 22- 28 22- 23 22- 22- 22- 24 22- 23 22- 22- --- 22- 22- 26 35+ --- 22- 24 80 : 22 23 26 22- 24 22- 24 22- 25 22- 24 22- 22- --- 22- 22- 25 37+ --- 22- 25 80 : 22 22- 26 22- 23 22- 22- 22- 25 22- 24 22- 22- --- 22- 23 25 37+ --- 22- 26 80 : 22 23 27 22- 23 22- 22- 22- 25 22- 24 23 23 --- 22- 22- 25 37+ --- 22- 27 80 : 22 22- 27 22- 22- 22- 22- 22- 26 22- 24 22- 22- --- 22- 22- 25 33+ --- 22- 28 80 : 22 23 27 22- 22- 22- 22- 22- 27 22- 24 22- 22- --- 22- 22- 26 33+ --- 22- 29 80 : 22 23 25 22- 22- 22- 22- 22- 25 22- 24 23 22- --- 22- 22- 26 34+ --- 22- 30 80 : 22 22- 25 22- 22- 22- 22- 22- 25 22- 24 23 22- --- 22- 23 24 34+ --- 22- 31 80 : 22 22- 30 22- 23 22- 23 22- 25 22- 25 22- 22- --- 22- 23 25 36+ --- 22- 32 80 : 22 23 28 22- 23 22- 23 22- 24 22- 25 22- 22- --- 22- 22- 26 36+ --- 22- 33 80 : 22 23 30 22- 23 22- 22- 22- 26 22- 25 22- 22- --- 22- 22- 26 36+ --- 22- Rank 1: Student 4 with score 0 Rank 1: Student 8 with score 0 Rank 1: Student 20 with score 0 Rank 4: Student 6 with score 1 Rank 5: Student 15 with score 5 Rank 6: Student 13 with score 31 Rank 7: Student 16 with score 39 Rank 8: Student 2 with score 41 Rank 8: Student 12 with score 41 ===================================== Rank 10: Student 7 with score 46 Rank 11: Student 10 with score 51 Rank 12: Student 5 with score 55 Rank 13: Student 11 with score 106 Rank 14: Student 17 with score 130 Rank 15: Student 9 with score 142 Rank 16: Student 3 with score 257 Rank 17: Student 18 with score 457 Rank 18: Student 14 with score 1775 Rank 19: Student 19 with score 2564 Football distance 1: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 9 : 3 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 2 27 : 5 5- 6 5- 5- 6 5- 5- 5- 5- 5- 5- 5- 5- 5- 5- 5- 7+ 5- 5- 3 81 : 9 9- 18 9- 27+ 9- 9- 27+ 15 20 14 9- 9- 15 9- 9- 14 21 13 9- 4 243 : 27 35 56 65 81+ 36 27- 81+ 39 78 41 36 31 38 39 35 41 61 41 33 5 729 : 73 105 152 235 243 99 93 243 107 241 112 105 92- 105 110 107 110 730+ 117 93 6 2187 : 186 302 473 725 729 292 245- 729 286 1667 320 303 2187+ 2187+ --- 300 311 --- --- 247 Rank 1: Student 7 with score 79 Rank 2: Student 20 with score 87 Rank 3: Student 6 with score 142 Rank 4: Student 9 with score 152 Rank 5: Student 2 with score 156 Rank 5: Student 16 with score 156 ===================================== Rank 7: Student 12 with score 158 Rank 8: Student 17 with score 181 Rank 9: Student 11 with score 192 Rank 10: Student 3 with score 405 Rank 11: Student 4 with score 739 Rank 12: Student 5 with score 785 Rank 12: Student 8 with score 785 Rank 14: Student 10 with score 1711 Rank 15: Student 13 with score 2024 Rank 16: Student 14 with score 2050 Rank 17: Student 15 with score 2236 Rank 18: Student 19 with score 2249 Rank 19: Student 18 with score 2892 Football distance 2: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 27 : 3 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 2 81 : 3 3- 6 3- 5 3- 3- 3- 5 3- 3- 3- 3- 5 3- 3- 4 9+ 3- 3- 3 243 : 8 9 16 12 27+ 11 9 27+ 12 21 10 9 9 12 9 9 11 9 9 8- 4 729 : 17 25 44 72 81 28 22 81 30 124 25 24 21- 31 30 26 28 730+ 25 21- 5 2187 : 34 65 133 237 243 72 52- 243 67 1757+ 71 64 56 69 --- 65 66 --- 70 53 Rank 1: Student 20 with score 23 Rank 2: Student 7 with score 24 Rank 3: Student 13 with score 27 Rank 4: Student 12 with score 38 Rank 5: Student 2 with score 40 ===================================== Rank 6: Student 16 with score 41 Rank 7: Student 19 with score 45 Rank 8: Student 11 with score 47 Rank 8: Student 17 with score 47 Rank 10: Student 6 with score 52 Rank 10: Student 9 with score 52 Rank 12: Student 14 with score 55 Rank 13: Student 3 with score 137 Rank 14: Student 4 with score 262 Rank 15: Student 8 with score 292 Rank 16: Student 5 with score 294 Rank 17: Student 10 with score 1843 Rank 18: Student 15 with score 2201 Rank 19: Student 18 with score 2907 Football distance 3: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 81 : 3 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- --- 3- 3- 3- 3- 3- 3- 3- 2 243 : 3 3- 7+ 3- 6 3- 3- --- 5 3- 3- 3- --- 5 3- 3- 3- 3- 3- 3- 3 729 : 6 7 12 13 27 6- 6- --- 10 244 7 8 --- 14 10 6- 9 730+ 7 6- 4 2187 : 12 19 29 78 81 31 16 --- 22 --- 19 18 --- 2187+ --- 18 20 --- 19 15- Rank 1: Student 20 with score 3 Rank 2: Student 7 with score 4 Rank 3: Student 16 with score 6 Rank 4: Student 2 with score 8 Rank 4: Student 11 with score 8 Rank 4: Student 12 with score 8 Rank 4: Student 19 with score 8 ===================================== Rank 8: Student 17 with score 11 Rank 9: Student 9 with score 16 Rank 10: Student 6 with score 19 Rank 11: Student 3 with score 27 Rank 12: Student 4 with score 73 Rank 13: Student 5 with score 93 Rank 14: Student 14 with score 2185 Rank 15: Student 15 with score 2191 Rank 16: Student 10 with score 2425 Rank 17: Student 18 with score 2911 Rank 18: Student 8 with score 3240 Rank 18: Student 13 with score 3240 Hypercube distance 1: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 8 : 2 2- 4+ 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 4+ 2- 2- 2 16 : 4 4- 5 4- 4- 5 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 8+ 4- 4- 3 32 : 7 7 10 7 10 8 7 7 8 7 7 6- 7 7 7 7 7 16+ 7 7 4 64 : 12 12- 19 12- 22 16 13 16 15 16 12- 12- 12- 14 12- 12- 14 32+ 12- 12- 5 128 : 16 16- 44 34 48 16- 16- 38 25 50 26 22 17 28 23 20 27 64+ 27 16- 6 256 : 32 45 102 99 128+ 41 32- 102 47 118 50 44 38 48 46 45 48 128+ 49 39 7 512 : 62 88 184 233 256+ 82 71- 232 89 249 94 89 78 95 86 87 95 256+ 92 75 8 1024 : 120 169 372 495 512 162 143- 490 168 509 180 171 151 171 174 171 177 1025+ 183 147 9 2048 : 192 335 764 1012 1024 308 270- 1006 307 1511 339 325 2048+ 331 --- 330 337 --- --- 277 Rank 1: Student 7 with score 111 Rank 2: Student 20 with score 132 Rank 3: Student 6 with score 193 Rank 4: Student 9 with score 218 Rank 5: Student 12 with score 228 Rank 6: Student 2 with score 231 Rank 6: Student 16 with score 231 ===================================== Rank 8: Student 14 with score 253 Rank 9: Student 17 with score 264 Rank 10: Student 11 with score 267 Rank 11: Student 3 with score 1057 Rank 12: Student 8 with score 1450 Rank 13: Student 4 with score 1451 Rank 14: Student 5 with score 1559 Rank 15: Student 13 with score 1910 Rank 16: Student 10 with score 2019 Rank 17: Student 15 with score 2147 Rank 18: Student 19 with score 2169 Rank 19: Student 18 with score 3326 Hypercube distance 2: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 32 : 2 2- 4+ 2- 2- 2- 2- 2- 4+ 2- 2- 2- 2- 4+ 2- 2- 2- 4+ 2- 2- 2 64 : 4 4- 8+ 4- 4- 6 4- 4- 5 4- 4- 4- 4- 5 4- 4- 4- 8+ 4- 4- 3 128 : 7 7- 17 7- 19+ 8 7- 16 7- 8 8 7- 7- 11 7- 7- 8 16 7- 7- 4 256 : 12 13 35 18 46+ 16 12- 39 14 36 15 13 12- 18 14 12- 15 16 14 12- 5 512 : 16 24 74 75 116+ 27 22- 102 26 116+ 29 24 22- 28 28 24 26 32 26 22- 6 1024 : 30 45 141 216 256 49 37- 232 49 448 48 46 38 51 44 46 47 1025+ 45 37- 7 2048 : 44 81 284 493 512 84 64- 490 84 1589 87 84 70 2048+ --- 82 84 --- 86 65 Rank 1: Student 7 with score 33 Rank 2: Student 20 with score 34 Rank 3: Student 13 with score 40 Rank 4: Student 2 with score 61 ===================================== Rank 5: Student 16 with score 62 Rank 6: Student 12 with score 65 Rank 7: Student 19 with score 69 Rank 8: Student 17 with score 71 Rank 9: Student 9 with score 74 Rank 10: Student 6 with score 77 Rank 11: Student 11 with score 78 Rank 12: Student 3 with score 448 Rank 13: Student 4 with score 700 Rank 14: Student 8 with score 770 Rank 15: Student 5 with score 840 Rank 16: Student 14 with score 2050 Rank 17: Student 15 with score 2076 Rank 18: Student 10 with score 2088 Rank 19: Student 18 with score 3078 Hypercube distance 3: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 128 : 2 2- 6 2- 2- 2- 2- 2- 4 2- 2- 2- --- 4 2- 2- 2- 8+ 2- 2- 2 256 : 4 4- 7 4- 18+ 7 4- 16 4- 4- 4- 4- --- 8 4- 4- 4- 16 4- 4- 3 512 : 7 8 16 9 40 9 7- 40 10 42+ 8 8 --- 11 9 8 9 16 8 7- 4 1024 : 12 15 32 91 105 18 13 105 16 562 19 15 --- 19 21 15 17 1025+ 16 12- 5 2048 : 16 26 56 246 242 40 22- 237 28 1681 27 26 --- 2048+ --- 27 29 --- 27 22- Rank 1: Student 20 with score 6 Rank 2: Student 7 with score 7 Rank 3: Student 2 with score 14 Rank 3: Student 12 with score 14 ===================================== Rank 5: Student 16 with score 15 Rank 6: Student 19 with score 16 Rank 7: Student 11 with score 19 Rank 8: Student 17 with score 20 Rank 9: Student 9 with score 21 Rank 10: Student 6 with score 35 Rank 11: Student 3 with score 76 Rank 12: Student 4 with score 311 Rank 13: Student 8 with score 359 Rank 14: Student 5 with score 366 Rank 15: Student 14 with score 2049 Rank 16: Student 15 with score 2059 Rank 17: Student 10 with score 2250 Rank 18: Student 18 with score 3088 Rank 19: Student 13 with score 3968 Kneser Graphs: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 35 : 7 7- 10+ 7- 7- 7- 7- 7- 10+ 7- 7- 7- 7- 10+ 7- 7- 7- 10+ 7- 7- 2 56 : 7 7- 14 7- 16+ 9 7- 12 10 7- 7- 7- 7- 10 8 7- 9 10 7- 7- 3 84 : 7 7- 10 7- 19+ 7- 7- 16 9 7- 7- 7- 7- 10 7- 7- 8 10 7- 7- 4 120 : 6 6- 9 6- 22+ 7 6- 22+ 6- 6- 6- 6- 6- 10 6- 6- 7 10 6- 6- 5 165 : 5 5- 8 5- 25+ 7 5- 25+ 9 5- 5- 5- 5- 9 5- 5- 6 10 5- 5- 6 220 : 4 4- 7 4- 28+ 7 4- 28+ 7 5 4- 4- 4- 9 4- 4- 5 10 4- 4- 7 286 : 4 4- 7 4- 31+ 7 4- 31+ 6 5 4- 4- 4- 8 6 4- 4- 10 4- 4- 8 126 : 26 28 35 34 56+ 31 28 48 33 35 29 29 28 34 30 28 31 35 32 27- 9 210 : 15 22 35 29 84+ 24 18 70 26 35 27 21 16- 31 26 23 26 35 26 22 10 330 : 15 19 31 24 101+ 22 17 101+ 23 35 21 20 17 38 22 19 22 35 22 16- 11 495 : 12 17 27 18 131+ 19 14- 131+ 20 33 17 17 14- 35 20 16 18 35 17 14- 12 715 : 10 15 19 19 165 16 13- 165 16 141 15 15 13- 32 17 15 16 716+ 15 14 13 462 : 66 103 126 125 210+ 91 94 203 106 126 113 104 92 108 106 102 107 126 112 90- 14 792 : 56 78 121 125 330 102 69 316 85 126 86 78 70 82 96 80 84 793+ 82 68- 15 1287 : 39 61 102 125 461 85 51 461 63 720 63 59 51 81 96 60 64 1288+ 63 50- Rank 1: Student 13 with score 62 Rank 1: Student 20 with score 62 Rank 3: Student 7 with score 65 Rank 4: Student 2 with score 104 Rank 4: Student 12 with score 104 Rank 4: Student 16 with score 104 ===================================== Rank 7: Student 19 with score 130 Rank 8: Student 11 with score 132 Rank 9: Student 17 with score 135 Rank 10: Student 9 with score 150 Rank 11: Student 6 with score 162 Rank 12: Student 15 with score 177 Rank 13: Student 14 with score 228 Rank 14: Student 4 with score 260 Rank 15: Student 3 with score 282 Rank 16: Student 10 with score 1014 Rank 17: Student 8 with score 1357 Rank 18: Student 5 with score 1407 Rank 19: Student 18 with score 2854 Queen Graphs: # n : k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 k 9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 1 16 : 2 2- 2- 2- 3+ 3+ 2- 2- 2- 2- 2- 2- 2- 3+ 2- 2- 2- 2- 2- 2- 2 25 : 3 3- 3- 3- 4+ 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- 3 36 : 3 3- 4 3- 5+ 3- 3- 3- 4 3- 3- 3- 3- 5+ 3- 4 4 4 3- 3- 4 49 : 4 4- 6+ 4- 4- 4- 4- 4- 5 4- 4- 4- 4- 5 4- 4- 5 5 4- 4- 5 64 : 5 5- 6+ 5- 5- 5- 5- 5- 6+ 5- 5- 5- 5- 6+ 5- 5- 6+ 6+ 5- 5- 6 81 : 5 5- 6 5- 6 5- 5- 6 7+ 6 5- 5- 5- 7+ 6 5- 6 6 5- 5- 7 100 : 5 5- 8 5- 9+ 5- 5- 6 7 7 6 7 5- 8 7 6 8 7 6 5- 8 121 : 5 5- 9 5- 10+ 5- 6 9 10+ 8 7 6 5- 10+ 8 5- 7 7 7 5- 9 144 : 6 8 9 6- 11+ 8 7 11+ 8 10 8 8 7 11+ 9 7 10 8 7 7 10 169 : 7 8 10 8 12+ 8 8 12+ 8 11 9 9 7- 10 10 7- 9 9 7- 7- 11 196 : 8 9 10 11 13+ 9 8- 13+ 9 12 10 9 8- 12 11 10 11 9 8- 8- 12 225 : 9 10 10 12 14 10 9- 14 12 13 11 11 9- 15+ 12 10 12 10 9- 9- 13 256 : 9 11 12 13 15 12 10 15 11 14 12 11 10 16+ 13 11 12 11 10 9- 14 289 : 9 13 13 15 16 12 11 16 12 15 14 12 11 17+ 14 12 14 13 11 10- 15 324 : 9 14 15 16 17+ 13 11 17+ 14 16 15 13 11 16 15 14 16 12 11 10- 16 361 : 10 14 15 17 18 16 12 18 14 17 15 14 12 20+ 16 15 17 15 14 11- 17 400 : 11 16 15 18 19 16 12- 19 16 18 17 15 12- 21+ 16 15 18 16 13 12- 18 441 : 11 17 16 19 20 17 14 20 20 19 17 17 13- 23+ 20 16 18 15 16 13- 19 484 : 12 18 18 20 21 19 14- 21 16 20 19 17 14- 24+ 19 18 19 16 15 14- 20 529 : 12 19 19 21 22 20 15 22 20 21 20 18 15 25+ 25+ 18 21 17 17 14- 21 576 : 13 20 21 22 23 22 15 23 18 22 22 19 16 27+ 24 20 21 19 20 14- 22 625 : 13 22 21 23 24 23 17 24 19 24 23 20 17 --- 27+ 21 22 19 20 16- 23 676 : 14 21 22 24 25 24 17 25 20 88+ 23 21 18 --- 29 23 24 22 22 16- 24 729 : 14 23 24 25 26 25 18 26 23 157 24 23 18 --- 28 24 26 730+ 24 16- 25 784 : 15 25 24 26 27 27 19 27 21 226 25 24 19 --- 34 24 26 785+ 24 16- 26 841 : 15 25 24 27 28 29 20 28 22 295 28 25 20 --- 31 25 27 842+ 23 17- 27 900 : 15 27 25 28 29 28 21 29 24 368 25 27 21 --- 34 27 26 901+ 28 18- Rank 1: Student 20 with score 25 Rank 2: Student 13 with score 46 Rank 3: Student 7 with score 47 Rank 4: Student 19 with score 90 Rank 5: Student 12 with score 104 Rank 6: Student 9 with score 107 Rank 6: Student 16 with score 107 Rank 8: Student 2 with score 108 ===================================== Rank 9: Student 3 with score 123 Rank 10: Student 6 with score 127 Rank 11: Student 11 with score 128 Rank 12: Student 4 with score 139 Rank 13: Student 17 with score 146 Rank 14: Student 8 with score 174 Rank 15: Student 15 with score 181 Rank 16: Student 5 with score 182 Rank 17: Student 10 with score 1160 Rank 18: Student 18 with score 3265 Rank 19: Student 14 with score 4681