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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 1 80 : 20 22- 27 25 22- 23 80+ --- 24 27 23 --- 22- 26 22- 22- 22- --- --- 2 80 : 20 22- 27 --- 23 22- 80+ --- 25 26 23 --- 22- 26 22- 22- 25 --- --- 3 80 : 20 22- 24 --- 22- 22- 80+ --- 24 26 24 --- 22- 28 22- 22- 27 --- --- 4 80 : 20 22- 24 --- 22- 22- 80+ --- 25 25 24 --- 22- 27 23 22- 26 --- --- 5 80 : 20 23 24 --- 22- 23 80+ --- 23 27 25 --- 22- 26 22- 22- 26 --- --- 6 80 : 20 22- 28 --- 22- 23 80+ --- 25 27 24 --- 22- 27 22- 22- 27 --- --- 7 80 : 20 22- 27 --- 22- 22- 80+ --- 25 25 25 --- 23 26 22- 22- 28 --- --- 8 80 : 20 22- 26 --- 22- 22- 80+ --- 24 27 25 --- 22- 25 22- 22- 28 --- --- 9 80 : 20 22 27 --- 23 20- 80+ --- 25 27 24 --- 22 28 22 22 25 --- --- 10 80 : 20 22- 28 --- 23 22- 80+ --- 25 26 25 --- 22- 26 22- 22- 27 --- --- 11 80 : 20 22 27 --- 22 22 80+ --- 24 26 26 --- 22 29 22 20- 27 --- --- 12 80 : 21 23 26 --- 23 23 80+ --- 23 27 26 --- 22- 26 23 22- 26 --- --- 13 80 : 21 22 27 --- 23 22 80+ --- 24 27 25 --- 22 25 23 21- 28 --- --- 14 80 : 21 22- 23 --- 23 23 80+ --- 24 25 25 --- 22- 28 22- 23 28 --- --- 15 80 : 21 22- 27 --- 23 23 80+ --- 26 27 25 --- 22- 28 23 22- 28 --- --- 16 80 : 21 22- 26 --- 23 22- 80+ --- 26 27 25 --- 23 25 23 22- 27 --- --- 17 80 : 21 22- 26 --- 23 23 80+ --- 26 24 24 --- 22- 26 23 23 26 --- --- 18 80 : 21 23 26 --- 23 23 80+ --- 26 24 25 --- 22- 26 22- 22- 25 --- --- 19 80 : 21 22- 25 --- 23 22- 80+ --- 25 26 24 --- 22- 26 22- 22- 25 --- --- 20 80 : 21 22- 26 --- 23 22- 80+ --- 24 27 24 --- 23 28 23 22- 25 --- --- 21 80 : 21 23 25 --- 23 23 80+ --- 24 26 24 --- 22- 26 22- 22- 25 --- --- 22 80 : 21 22- 25 --- 23 22- 80+ --- 24 26 24 --- 22- 26 23 23 26 --- --- 23 80 : 22 22- 25 --- 23 23 80+ --- 25 25 24 --- 22- 25 23 23 26 --- --- 24 80 : 22 23 25 --- 24 23 80+ --- 23 26 24 --- 22- 26 23 22- 27 --- --- 25 80 : 22 22- 29 --- 23 23 80+ --- 24 27 25 --- 22- 27 23 22- 26 --- --- 26 80 : 22 23 29 --- 23 23 80+ --- 26 27 24 --- 22- 27 22- 22- 26 --- --- 27 80 : 22 22- 29 --- 22- 22- 80+ --- 26 27 24 --- 22- 27 22- 22- 28 --- --- 28 80 : 22 23 28+ --- 22- 22- --- --- 26 27 24 --- 22- 25 23 22- 25 --- --- 29 80 : 22 22- 26 --- 22- 23 --- --- 25 27+ 24 --- 23 27+ 22- 22- 26 --- --- 30 80 : 22 22- 26 --- 22- 23 --- --- 24 28 24 --- 23 24 22- 22- 30+ --- --- 31 80 : 22 22- 26 --- 23 22- --- --- 24 26 24 --- 23 28+ 22- 22- 25 --- --- 32 80 : 22 23 26 --- 23 22- --- --- 27 26 24 --- 22- 29+ 23 22- 27 --- --- 33 80 : 22 23 27+ --- 23 22- --- --- 26 25 24 --- 23 26 22- 22- 27+ --- --- Rank 1: Student 16 with score 34 Rank 2: Student 13 with score 40 Rank 3: Student 2 with score 42 ===================================== Rank 4: Student 6 with score 46 Rank 4: Student 15 with score 46 Rank 6: Student 5 with score 55 Rank 7: Student 11 with score 111 Rank 8: Student 9 with score 124 Rank 9: Student 10 with score 173 Rank 10: Student 3 with score 174 Rank 11: Student 17 with score 177 Rank 12: Student 14 with score 182 Rank 13: Student 7 with score 2079 Rank 14: Student 4 with score 2565 Rank 15: Student 8 with score 2640 Rank 15: Student 12 with score 2640 Rank 15: Student 18 with score 2640 Rank 15: Student 19 with score 2640 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 1 9 : 3 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- 3- --- 3- 2 27 : 5 5- 7+ --- 5- 5- 5- 5- 5- 5- 5- --- 5- 5- 5- 5- 7+ --- 5- 3 81 : 9 9- 15 --- 27+ 9- 16 12 9- 16 12 --- 9- 16 9- 9- 17 --- 14 4 243 : 27 36 40 --- 81 36 243+ 41 40 38 42 --- 35- 43 36 35- 42 --- 41 5 729 : 73 107 114 --- 243 108 729+ 112 112 118 112 --- 106 115 109 104- 116 --- 113 6 2187 : 186 306 309 --- 729+ 305 --- 326 316 309 311 --- --- 316 302- 303 321 --- 315 Rank 1: Student 16 with score 156 Rank 2: Student 15 with score 161 Rank 3: Student 2 with score 163 Rank 3: Student 6 with score 163 ===================================== Rank 5: Student 9 with score 182 Rank 5: Student 11 with score 182 Rank 7: Student 3 with score 185 Rank 8: Student 10 with score 186 Rank 9: Student 19 with score 188 Rank 10: Student 14 with score 195 Rank 11: Student 8 with score 196 Rank 12: Student 17 with score 203 Rank 13: Student 5 with score 785 Rank 14: Student 13 with score 2228 Rank 15: Student 7 with score 3066 Rank 16: Student 4 with score 3267 Rank 17: Student 12 with score 3276 Rank 17: Student 18 with score 3276 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 1 27 : 3 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- 3- --- 3- 2 81 : 3 3- 6+ --- 4 3- 3- 3- 3- 3- 3- --- 3- 6+ 3- 3- 6+ --- 3- 3 243 : 8 9- 12 --- 27+ 9- 11 10 9- 12 10 --- 9- 13 10 9- 11 --- 9- 4 729 : 17 25 30 --- 81 24- 729+ 28 26 27 28 --- 24- 28 25 24- 29 --- 26 5 2187 : 34 67 69 --- 243 67 2187+ 67 66- 70 68 --- --- 73 67 66- 69 --- 66- Rank 1: Student 16 with score 40 Rank 2: Student 6 with score 41 Rank 3: Student 2 with score 42 Rank 3: Student 9 with score 42 Rank 3: Student 19 with score 42 ===================================== Rank 6: Student 15 with score 43 Rank 7: Student 8 with score 46 Rank 8: Student 11 with score 47 Rank 9: Student 10 with score 50 Rank 10: Student 17 with score 53 Rank 11: Student 3 with score 55 Rank 12: Student 14 with score 58 Rank 13: Student 5 with score 293 Rank 14: Student 13 with score 2195 Rank 15: Student 7 with score 2868 Rank 16: Student 4 with score 3240 Rank 17: Student 12 with score 3267 Rank 17: Student 18 with score 3267 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 1 81 : 3 3- 3- 3- 3- 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- 3- --- 3- 2 243 : 3 3- 5 --- 6+ 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- 6+ --- 3- 3 729 : 6 7 10 --- 27+ 8 9 6- 10 11 7 --- 7 10 7 6- 11 --- 7 4 2187 : 12 20 21 --- 81+ 19 27 19 19 19 19 --- --- 21 19 18- 22 --- 19 Rank 1: Student 16 with score 6 Rank 2: Student 8 with score 7 Rank 3: Student 11 with score 8 Rank 3: Student 15 with score 8 Rank 3: Student 19 with score 8 Rank 6: Student 2 with score 9 Rank 6: Student 6 with score 9 ===================================== Rank 8: Student 9 with score 11 Rank 9: Student 10 with score 12 Rank 10: Student 14 with score 13 Rank 11: Student 3 with score 15 Rank 12: Student 7 with score 18 Rank 12: Student 17 with score 18 Rank 14: Student 5 with score 93 Rank 15: Student 13 with score 2188 Rank 16: Student 4 with score 3159 Rank 17: Student 12 with score 3240 Rank 17: Student 18 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 1 8 : 2 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- --- 2- 4+ 2- 2- 2- --- --- 2 16 : 4 4- 4- --- 4- 4- 4- 4- 4- 4- 4- --- 4- 4- 4- 4- 5+ --- --- 3 32 : 7 7- 7- --- 8 7- 7- 7- 7- 7- 7- --- 7- 8 7- 7- 9+ --- --- 4 64 : 12 12- 16 --- 16 12- 64+ 12- 13 14 13 --- 12- 15 12- 12- 14 --- --- 5 128 : 16 20 27 --- 40 21 128+ 25 25 26 24 --- 16- 28 22 20 30 --- --- 6 256 : 32 42- 50 --- 128 45 256+ 52 51 48 49 --- 43 48 45 45 51 --- --- 7 512 : 62 87 94 --- 256+ 90 --- 98 94 95 94 --- 86- 97 87 88 97 --- --- 8 1024 : 120 170- 183 --- 512+ 173 --- 179 176 171 180 --- --- 176 172 171 188 --- --- 9 2048 : 192 334 329 --- 1024+ 336 --- 339 334 336 339 --- --- 328 327 326- 343 --- --- Rank 1: Student 16 with score 228 Rank 2: Student 2 with score 231 Rank 2: Student 15 with score 231 ===================================== Rank 4: Student 6 with score 243 Rank 5: Student 10 with score 256 Rank 6: Student 9 with score 259 Rank 7: Student 14 with score 261 Rank 8: Student 3 with score 265 Rank 8: Student 11 with score 265 Rank 10: Student 8 with score 271 Rank 11: Student 17 with score 292 Rank 12: Student 5 with score 1543 Rank 13: Student 13 with score 3107 Rank 14: Student 7 with score 3972 Rank 15: Student 4 with score 4080 Rank 16: Student 12 with score 4088 Rank 16: Student 18 with score 4088 Rank 16: Student 19 with score 4088 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 1 32 : 2 2- 4+ 2- 2- 2- 2- 2- 2- 2- 2- --- 2- 2- 2- 2- 2- --- 2- 2 64 : 4 4- 5+ --- 4- 4- 4- 4- 4- 4- 4- --- 4- 5+ 4- 4- 5+ --- 4- 3 128 : 7 7- 8 --- 16+ 7- 8 7- 7- 8 7- --- 7- 8 7- 7- 9 --- 7- 4 256 : 12 13 15 --- 39+ 13 16 12- 13 16 14 --- 13 17 13 13 16 --- 15 5 512 : 16 24- 27 --- 105 24- 512+ 29 31 26 25 --- 24- 31 25 24- 28 --- 26 6 1024 : 30 45- 50 --- 237 46 1024+ 47 50 46 49 --- --- 45- 46 45- 49 --- 47 7 2048 : 44 83 87 --- 512 84 2048+ 89 89 86 89 --- --- 87 83 82- 85 --- 86 Rank 1: Student 16 with score 62 Rank 2: Student 2 with score 63 ===================================== Rank 3: Student 6 with score 65 Rank 3: Student 15 with score 65 Rank 5: Student 19 with score 72 Rank 6: Student 10 with score 73 Rank 7: Student 8 with score 75 Rank 7: Student 11 with score 75 Rank 9: Student 17 with score 79 Rank 10: Student 14 with score 80 Rank 11: Student 3 with score 81 Rank 11: Student 9 with score 81 Rank 13: Student 5 with score 800 Rank 14: Student 13 with score 3081 Rank 15: Student 7 with score 3499 Rank 16: Student 4 with score 4032 Rank 17: Student 12 with score 4064 Rank 17: Student 18 with score 4064 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 1 128 : 2 2- 5+ 2- 2- 2- 2- 2- 2- 4 2- --- 2- 4 2- 2- 2- --- 2- 2 256 : 4 4- 4- --- 16+ 4- 4- 4- 4- 7 4- --- 4- 6 4- 4- 6 --- 4- 3 512 : 7 8- 11 --- 40+ 8- 10 8- 8- 9 8- --- 8- 11 8- 8- 8- --- 8- 4 1024 : 12 15 17 --- 108+ 16 19 16 15 17 17 --- --- 18 15 14- 16 --- 16 5 2048 : 16 28 26- --- 237 29 2048+ 30 28 30 27 --- --- 31 28 26- 30 --- 29 Rank 1: Student 16 with score 13 Rank 2: Student 2 with score 16 Rank 2: Student 9 with score 16 Rank 2: Student 15 with score 16 ===================================== Rank 5: Student 11 with score 17 Rank 6: Student 6 with score 18 Rank 6: Student 19 with score 18 Rank 8: Student 8 with score 19 Rank 9: Student 17 with score 21 Rank 10: Student 3 with score 22 Rank 11: Student 10 with score 26 Rank 12: Student 14 with score 29 Rank 13: Student 5 with score 362 Rank 14: Student 7 with score 2042 Rank 15: Student 13 with score 3073 Rank 16: Student 4 with score 3840 Rank 17: Student 12 with score 3968 Rank 17: Student 18 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 1 35 : 7 7- 11+ 7- 10 7- 8 7- 7- 10 7- --- 7- 10 7- 7- 7- --- 7- 2 56 : 7 7- 9 --- 12+ 7- 8 7- 7- 9 7- --- 7- 10 7- 7- 10 --- 7- 3 84 : 7 7- 8 --- 19+ 7- 7- 7- 7- 8 7- --- 7- 8 7- 7- 9 --- 7- 4 120 : 6 6- 7 --- 22+ 6- 6- 6- 6- 8 6- --- 6- 7 6- 6- 7 --- 6- 5 165 : 5 5- 6 --- 25+ 5- 5- 5- 5- 7 5- --- 5- 7 5- 5- 8 --- 5- 6 220 : 4 4- 8 --- 28+ 4- 4- 4- 4- 6 4- --- 4- 6 4- 4- 6 --- 4- 7 286 : 4 4- 5 --- 31+ 4- 4- 4- 4- 4- 4- --- 4- 7 4- 4- 6 --- 4- 8 126 : 26 29 34 --- 56 28- 126+ 35 34 33 31 --- 29 37 28- 29 38 --- 30 9 210 : 15 23 30 --- 70 24 210+ 26 27 28 26 --- 21- 27 24 24 29 --- 25 10 330 : 15 19- 23 --- 101+ 20 26 22 19- 23 22 --- 19- 22 20 19- 22 --- 22 11 495 : 12 17 21 --- 131+ 17 21 17 17 18 18 --- 16- 21 16- 16- 22 --- 17 12 715 : 10 15 19 --- 165+ 15 19 17 15 19 15 --- 14- 15 15 15 18 --- 15 13 462 : 66 104 115 --- 210 104 462+ 112 109 110 113 --- 102- 112 104 104 116 --- 112 14 792 : 56 80 87 --- 330 79- 792+ 82 82 83 87 --- 80 87 79- 79- 86 --- 82 15 1287 : 39 59- 62 --- 461+ 61 --- 64 64 64 62 --- --- 64 60 59- 67 --- 63 Rank 1: Student 16 with score 106 Rank 2: Student 2 with score 107 Rank 2: Student 15 with score 107 ===================================== Rank 4: Student 6 with score 109 Rank 5: Student 19 with score 127 Rank 6: Student 9 with score 128 Rank 7: Student 11 with score 135 Rank 8: Student 8 with score 136 Rank 9: Student 10 with score 151 Rank 10: Student 14 with score 161 Rank 11: Student 3 with score 166 Rank 12: Student 17 with score 172 Rank 13: Student 13 with score 1368 Rank 14: Student 5 with score 1392 Rank 15: Student 7 with score 2745 Rank 16: Student 4 with score 5348 Rank 17: Student 12 with score 5383 Rank 17: Student 18 with score 5383 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 1 16 : 2 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- --- 2- 3+ 2- 2- 2- --- 2- 2 25 : 3 3- 3- --- 3- 3- 3- 3- 3- 3- 3- --- 3- 3- 3- 3- 3- --- 3- 3 36 : 3 3- 4 --- 4 3- 3- 3- 3- 5+ 3- --- 3- 5+ 3- 3- 4 --- 3- 4 49 : 4 4- 5 --- 4- 4- 4- 4- 4- 5 4- --- 4- 5 4- 4- 6+ --- 4- 5 64 : 5 5- 7+ --- 5- 5- 5- 5- 5- 5- 5- --- 5- 5- 5- 5- 7+ --- 5- 6 81 : 5 5- 8+ --- 8+ 5- 6 5- 5- 7 5- --- 5- 7 5- 5- 8+ --- 5- 7 100 : 5 6 8 --- 9+ 6 6 6 6 9+ 5- --- 5- 9+ 5- 5- 8 --- 5- 8 121 : 5 6- 10+ --- 9 7 8 7 7 9 7 --- 7 10+ 7 6- 10+ --- 8 9 144 : 6 8 10 --- 11+ 8 9 8 8 10 7- --- 8 10 8 8 10 --- 8 10 169 : 7 8- 12 --- 12 8- 10 9 9 11 9 --- 8- 13+ 9 8- 13+ --- 9 11 196 : 8 9- 13 --- 13 10 13 10 10 13 11 --- 9- 14+ 10 9- 12 --- 10 12 225 : 9 11 13 --- 14+ 11 13 11 11 12 11 --- 10- 12 11 11 13 --- 11 13 256 : 9 11- 13 --- 15+ 12 14 12 12 14 12 --- 11- 14 12 12 15+ --- 12 14 289 : 9 12- 14 --- 16+ 13 14 14 13 15 13 --- 12- 14 12- 12- 15 --- 13 15 324 : 9 13- 16 --- 17 14 17 14 15 16 15 --- 13- 18+ 14 13- 17 --- 15 16 361 : 10 14- 16 --- 18 15 17 16 16 17 16 --- 15 19 15 14- 20+ --- 16 17 400 : 11 16 17 --- 19 16 400+ 17 17 18 17 --- 15- 19 16 15- 20 --- 17 18 441 : 11 17 20 --- 20 17 20 17 17 20 18 --- 17 18 17 16- 21+ --- 17 19 484 : 12 18 21 --- 21 18 25+ 19 19 21 19 --- 17- 20 18 17- 19 --- 18 20 529 : 12 19 22 --- 22 19 23+ 20 18- 22 21 --- 18- 23+ 19 19 21 --- 20 21 576 : 13 20 23 --- 23 20 26+ 21 21 23 22 --- 19- 24 20 20 21 --- 21 22 625 : 13 21 25 --- 24 21 27+ 22 24 25 23 --- 20- 24 21 20- 25 --- 22 23 676 : 14 22 26 --- 25 22 676+ 22 26 25 23 --- 21- 27 22 21- 26 --- 24 24 729 : 14 23- 26 --- 26 24 29+ 25 24 24 24 --- 23- 26 24 23- 26 --- 24 25 784 : 15 24 28 --- 27 24 --- 24 25 27 28 --- 24 29+ 23- 24 27 --- 25 26 841 : 15 24- 28 --- 28 26 --- 26 27 29 26 --- 25 27 25 25 31+ --- 28 27 900 : 15 26- 30 --- 29 26- --- 28 28 27 26- --- 26- 29 27 26- 31+ --- 29 Rank 1: Student 13 with score 101 Rank 2: Student 16 with score 102 Rank 3: Student 2 with score 106 ===================================== Rank 4: Student 15 with score 113 Rank 5: Student 6 with score 115 Rank 6: Student 8 with score 126 Rank 7: Student 19 with score 130 Rank 8: Student 9 with score 131 Rank 8: Student 11 with score 131 Rank 10: Student 10 with score 170 Rank 11: Student 3 with score 176 Rank 12: Student 5 with score 180 Rank 13: Student 14 with score 183 Rank 14: Student 17 with score 187 Rank 15: Student 7 with score 3696 Rank 16: Student 4 with score 9425 Rank 17: Student 12 with score 9441 Rank 17: Student 18 with score 9441