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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 20- 28 20- 22 20- 80+ 20- 23 24 --- --- 20- 24 20- 20- 20- --- --- 2 80 : 20 20- 26 --- 23 20- 80+ 20- 22 26 --- --- 20- 26 20- 20- 25 --- --- 3 80 : 20 20- 25 --- 22 20- 80+ 20- 23 29 --- --- 20- 24 20- 20- 24 --- --- 4 80 : 20 20- 27 --- 22 20- 80+ 20- 22 28 --- --- 20- 22 20- 20- 24 --- --- 5 80 : 20 20- 25 --- 22 20- 80+ 20- 22 80+ --- --- 20- 25 20- 20- 25 --- --- 6 80 : 20 20- 26 --- 22 20- 80+ 20- 22 27 --- --- 20- 23 20- 20- 24 --- --- 7 80 : 20 20- 25 --- 22 20- 80+ 20- 22 26 --- --- 20- 23 20- 20- 25 --- --- 8 80 : 20 20- 27 --- 22 20- 80+ 20- 22 31 --- --- 20- 23 20- 20- 23 --- --- 9 80 : 20 20- 28 --- 23 20- 80+ 20- 22 80+ --- --- 20- 23 20- 20- 24 --- --- 10 80 : 20 20- 26 --- 23 20- 80+ 20- 22 80+ --- --- 20- 23 20- 20- 25 --- --- 11 80 : 20 20- 29 --- 22 20- 80+ 20- 22 27 --- --- 20- 22 20- 20- 20- --- --- 12 80 : 21 21- 27 --- 23 21- 80+ 21- 23 80+ --- --- 21- 23 21- 21- 25 --- --- 13 80 : 21 21- 27 --- 23 21- 80+ 21- 22 27 --- --- 21- --- 21- 21- 22 --- --- 14 80 : 21 21- 29 --- 23 21- 80+ 21- 22 27 --- --- 21- --- 21- 21- 23 --- --- 15 80 : 21 21- 26 --- 23 21- 80+ 21- 21- 27 --- --- 21- --- 21- 21- 23 --- --- 16 80 : 21 21- 26 --- 23 21- 80+ 21- 22 80+ --- --- 21- --- 21- 21- 22 --- --- 17 80 : 21 21- 28 --- 23 21- 80+ 21- 22 27 --- --- 21- --- 21- 21- 23 --- --- 18 80 : 21 21- 27 --- 23 21- 80+ 21- 23 80+ --- --- 21- --- 21- 21- 23 --- --- 19 80 : 21 21- 26 --- 23 21- 80+ 21- 21- 80+ --- --- 21- --- 21- 21- 23 --- --- 20 80 : 21 21- 26 --- 23 21- 80+ 22 22 80+ --- --- 21- --- 21- 21- 24 --- --- 21 80 : 21 21- 26 --- 23 21- 80+ 21- 22 80+ --- --- 21- --- 21- 22 26 --- --- 22 80 : 21 21- 28 --- 23 21- 80+ 21- 22 25 --- --- 21- --- 21- 21- 24 --- --- 23 80 : 22 22- 26 --- 23 22- 80+ 22- 23 28 --- --- 22- --- 22- 22- 22- --- --- 24 80 : 22 22- 27 --- 22- 22- 80+ 22- 22- 29 --- --- 22- --- 22- 22- 24 --- --- 25 80 : 22 22- 26 --- 23 22- 80+ 22- 22- 28 --- --- 22- --- 22- 22- 24 --- --- 26 80 : 22 22- 27 --- 23 22- 80+ 22- 22- 29 --- --- 22- --- 22- 22- 23 --- --- 27 80 : 22 22- 26 --- 22- 22- 80+ 22- 22- 28 --- --- 22- --- 22- 22- 22- --- --- 28 80 : 22 22- 27 --- 22- 22- --- 22- 22- 80+ --- --- 22- --- 22- 22- 22- --- --- 29 80 : 22 22- 26 --- 22- 22- --- 22- 22- 80+ --- --- 22- --- 22- 22- 23 --- --- 30 80 : 22 22- 26+ --- 22- 22- --- 22- 22- 26+ --- --- 22- --- 22- 22- 24 --- --- 31 80 : 22 22- 25+ --- 23 22- --- 22- 22- 25+ --- --- 22- --- 22- 22- 24 --- --- 32 80 : 22 22- 25 --- 23 22- --- 22- 22- 26+ --- --- 22- --- 22- 22- 24 --- --- 33 80 : 22 22- 25 --- 23 22- --- 22- 22- 80+ --- --- 22- --- 22- 22- 23 --- --- Rank 1: Student 2 with score 0 Rank 1: Student 6 with score 0 Rank 1: Student 13 with score 0 Rank 1: Student 15 with score 0 ===================================== Rank 5: Student 8 with score 1 Rank 5: Student 16 with score 1 Rank 7: Student 9 with score 36 Rank 8: Student 5 with score 53 Rank 9: Student 17 with score 79 Rank 10: Student 3 with score 181 Rank 11: Student 10 with score 837 Rank 12: Student 14 with score 1720 Rank 13: Student 7 with score 2079 Rank 14: Student 4 with score 2560 Rank 15: Student 11 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- 10+ --- 2 27 : 5 5- 6 --- 5- 5- 5- 5- 5- 6 --- --- 5- 7 5- 5- 6 28+ --- 3 81 : 9 9- 17 --- 27 9- 81+ 9- 12 81+ --- --- 9- 13 9- 9- 17 --- --- 4 243 : 27 36 38 --- 81 37 243+ 44 43 243+ --- --- 35- 50 37 37 40 --- --- 5 729 : 73 104 118 --- 243 106 729+ 112 138 729+ --- --- 103 114 103 101- 113 --- --- 6 2187 : 186 290- 313 --- 729+ 293 --- 298 360 --- --- --- --- 301 299 308 308 --- --- Rank 1: Student 2 with score 144 ===================================== Rank 2: Student 6 with score 150 Rank 3: Student 15 with score 153 Rank 4: Student 16 with score 160 Rank 5: Student 8 with score 168 Rank 6: Student 17 with score 184 Rank 7: Student 14 with score 185 Rank 8: Student 3 with score 192 Rank 9: Student 9 with score 258 Rank 10: Student 5 with score 785 Rank 11: Student 13 with score 2225 Rank 12: Student 7 with score 3131 Rank 13: Student 10 with score 3132 Rank 14: Student 4 with score 3267 Rank 15: Student 18 with score 3270 Rank 16: Student 11 with score 3276 Rank 16: Student 12 with score 3276 Rank 16: Student 19 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- 2 81 : 3 3- 3- --- 4 3- 5 3- 3- 6+ --- --- 3- 6+ 3- 3- 5 --- 3- 3 243 : 8 9- 11 --- 27+ 10 11 10 11 13 --- --- 9- 14 9- 9- 10 --- 12 4 729 : 17 25- 31 --- 81 26 729+ 28 28 70 --- --- 26 27 26 26 27 --- 29 5 2187 : 34 70 74 --- 243 69 2187+ 75 79 77 --- --- --- 71 67- 71 71 --- 74 Rank 1: Student 15 with score 43 Rank 2: Student 2 with score 45 ===================================== Rank 3: Student 6 with score 46 Rank 4: Student 16 with score 47 Rank 5: Student 17 with score 51 Rank 6: Student 8 with score 54 Rank 7: Student 14 with score 56 Rank 7: Student 19 with score 56 Rank 9: Student 3 with score 57 Rank 10: Student 9 with score 59 Rank 11: Student 10 with score 104 Rank 12: Student 5 with score 293 Rank 13: Student 13 with score 2197 Rank 14: Student 7 with score 2870 Rank 15: Student 4 with score 3240 Rank 16: Student 11 with score 3267 Rank 16: Student 12 with score 3267 Rank 16: 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- 2 243 : 3 3- 5 --- 6+ 3- 3- --- 3- 4 --- --- 3- 6+ 3- 3- 5 --- 3- 3 729 : 6 8 10 --- 27 8 729+ --- 10 10 --- --- 6- 10 8 10 11 --- 9 4 2187 : 12 21- 21- --- 81 21- 2187+ --- 23 23 --- --- --- 26 24 24 24 --- 24 Rank 1: Student 2 with score 11 Rank 1: Student 6 with score 11 ===================================== Rank 3: Student 15 with score 14 Rank 4: Student 3 with score 15 Rank 4: Student 9 with score 15 Rank 4: Student 19 with score 15 Rank 7: Student 10 with score 16 Rank 7: Student 16 with score 16 Rank 9: Student 17 with score 19 Rank 10: Student 14 with score 21 Rank 11: Student 5 with score 93 Rank 12: Student 13 with score 2187 Rank 13: Student 7 with score 2898 Rank 14: Student 4 with score 3159 Rank 15: Student 8 with score 3240 Rank 15: Student 11 with score 3240 Rank 15: Student 12 with score 3240 Rank 15: 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- 2- 2- 2- 2- --- 2 16 : 4 4- 4- --- 4- 4- 4- 4- 4- 5 --- --- 4- 5 4- 4- 4- 17+ --- 3 32 : 7 7- 8 --- 8 7- 7- 7- 7- 9 --- --- 7- 9 7- 7- 12 33+ --- 4 64 : 12 12- 15 --- 16 12- 64+ 12- 12- 64+ --- --- 12- 15 12- 12- 14 --- --- 5 128 : 16 22 28 --- 51 16- 128+ 23 23 28 --- --- 21 26 21 20 30 --- --- 6 256 : 32 44 56 --- 128 41- 256+ 48 63 256+ --- --- 41- 52 41- 44 53 --- --- 7 512 : 62 85- 97 --- 256 87 512+ 89 116 99 --- --- 85- 89 87 89 98 --- --- 8 1024 : 120 164 177 --- 512+ 164 --- 172 326 --- --- --- --- 174 163- 175 171 --- --- 9 2048 : 192 316- 343 --- 1024+ 319 --- 323 394 --- --- --- --- 333 318 337 329 --- --- Rank 1: Student 6 with score 205 Rank 2: Student 15 with score 208 Rank 3: Student 2 with score 209 ===================================== Rank 4: Student 8 with score 233 Rank 5: Student 16 with score 243 Rank 6: Student 14 with score 258 Rank 7: Student 17 with score 266 Rank 8: Student 3 with score 283 Rank 9: Student 9 with score 500 Rank 10: Student 5 with score 1554 Rank 11: Student 13 with score 3109 Rank 12: Student 10 with score 3400 Rank 13: Student 7 with score 3910 Rank 14: Student 18 with score 4071 Rank 15: Student 4 with score 4080 Rank 16: Student 11 with score 4088 Rank 16: Student 12 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- 4+ 2- 2- 2- --- 2- 2 64 : 4 4- 5 --- 4- 4- 4- 4- 4- 6+ --- --- 4- 6+ 4- 4- 5 --- 4- 3 128 : 7 7- 9 --- 16+ 7- 10 7- 7- 10 --- --- 7- 8 7- 7- 9 --- 7- 4 256 : 12 13 15 --- 40 13 256+ 13 13 30 --- --- 13 17 12- 13 16 --- 15 5 512 : 16 24- 28 --- 108 24- 512+ 25 28 28 --- --- 24- 27 25 24- 28 --- 26 6 1024 : 30 43- 51 --- 242 44 1024+ 50 52 50 --- --- --- 48 45 47 48 --- 49 7 2048 : 44 80- 92 --- 503 83 2048+ 86 86 92 --- --- --- 89 81 85 82 --- 90 Rank 1: Student 2 with score 58 ===================================== Rank 2: Student 15 with score 61 Rank 3: Student 6 with score 62 Rank 4: Student 16 with score 67 Rank 5: Student 8 with score 72 Rank 6: Student 17 with score 75 Rank 7: Student 9 with score 77 Rank 8: Student 19 with score 78 Rank 9: Student 14 with score 84 Rank 10: Student 3 with score 89 Rank 11: Student 10 with score 103 Rank 12: Student 5 with score 800 Rank 13: Student 13 with score 3081 Rank 14: Student 7 with score 3741 Rank 15: Student 4 with score 4032 Rank 16: Student 11 with score 4064 Rank 16: Student 12 with score 4064 Rank 16: 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- 2- 2- 2- 2- 2- 2- 2- 2- --- --- 2- 2- 2- 2- 2- --- 2- 2 256 : 4 4- 5 --- 16+ 4- 6 4- 4- 7 --- --- 4- 6 4- 4- 5 --- 4- 3 512 : 7 8 10 --- 40 9 512+ 7- 9 12 --- --- 7- 13 8 9 14 --- 10 4 1024 : 12 16 17 --- 108 15 1024+ 19 16 52 --- --- --- 18 14- 16 21 --- 16 5 2048 : 16 28 32 --- 237 28 2048+ 29 34 33 --- --- --- 31 27- 31 30 --- 31 Rank 1: Student 15 with score 14 Rank 2: Student 2 with score 17 Rank 2: Student 6 with score 17 ===================================== Rank 4: Student 8 with score 20 Rank 5: Student 16 with score 21 Rank 6: Student 19 with score 22 Rank 7: Student 9 with score 24 Rank 8: Student 3 with score 25 Rank 9: Student 14 with score 29 Rank 10: Student 17 with score 31 Rank 11: Student 10 with score 65 Rank 12: Student 5 with score 362 Rank 13: Student 13 with score 3072 Rank 14: Student 7 with score 3551 Rank 15: Student 4 with score 3840 Rank 16: Student 11 with score 3968 Rank 16: Student 12 with score 3968 Rank 16: 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- 10 7- 9 7- 8 7- 7- 10 --- --- 7- 10 7- 10 7- 36+ 7- 2 56 : 7 7- 9 --- 12+ 7- 8 7- 7- 10 --- --- 7- 10 7- 7- 9 --- 7- 3 84 : 7 7- 8 --- 16+ 7- 8 7- 7- 8 --- --- 7- 8 7- 7- 8 --- 7- 4 120 : 6 6- 6- --- 22+ 6- 6- 6- 6- 9 --- --- 6- 7 6- 6- 8 --- 6- 5 165 : 5 5- 8 --- 25+ 5- 5- 5- 5- 8 --- --- 5- 7 5- 5- 9 --- 5- 6 220 : 4 4- 7 --- 28+ 4- 4- 4- 4- 6 --- --- 4- 7 4- 4- 7 --- 4- 7 286 : 4 4- 5 --- 31+ 4- 4- 4- 4- 6 --- --- 4- 7 4- 4- 7 --- 4- 8 126 : 26 28- 35 --- 56 28- 126+ 32 35 33 --- --- 28- 32 29 29 35 --- 31 9 210 : 15 23- 28 --- 70 24 210+ 28 30 210+ --- --- 24 28 25 24 32 --- 27 10 330 : 15 19 22 --- 101 20 330+ 20 24 330+ --- --- 19 24 18- 19 26 --- 21 11 495 : 12 17 19 --- 131 17 495+ 17 19 20 --- --- 16- 20 18 18 22 --- 19 12 715 : 10 15 17 --- 165+ 16 19 15 16 19 --- --- 14- 17 15 15 18 --- 18 13 462 : 66 102 113 --- 210 104 462+ 107 113 462+ --- --- 101- 104 103 105 110 --- 111 14 792 : 56 86 82- --- 330 89 --- 105 140 792+ --- --- 84 105 88 86 99 --- 84 15 1287 : 39 66 62- --- 461+ 68 --- 84 87 65 --- --- --- 87 67 71 84 --- 65 Rank 1: Student 2 with score 117 ===================================== Rank 2: Student 15 with score 124 Rank 3: Student 6 with score 127 Rank 4: Student 16 with score 131 Rank 5: Student 19 with score 137 Rank 6: Student 3 with score 152 Rank 7: Student 8 with score 169 Rank 8: Student 14 with score 194 Rank 9: Student 17 with score 202 Rank 10: Student 9 with score 225 Rank 11: Student 13 with score 1373 Rank 12: Student 5 with score 1388 Rank 13: Student 10 with score 1709 Rank 14: Student 7 with score 3580 Rank 15: Student 4 with score 5348 Rank 16: Student 18 with score 5377 Rank 17: Student 11 with score 5383 Rank 17: Student 12 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- 3+ 2- 2- 2- 2- 2- 2 25 : 3 3- 3- --- 3- 3- 3- 3- 3- 5 --- --- 3- 3- 3- 3- 5 26+ 3- 3 36 : 3 3- 4 --- 4 3- 4 3- 3- 4 --- --- 3- 5+ 3- 3- 5+ --- 3- 4 49 : 4 4- 4- --- 4- 4- 5 4- 4- 6+ --- --- 4- 6+ 4- 4- 5 --- 4- 5 64 : 5 5- 6 --- 6 5- 6 5- 5- 5- --- --- 5- 8+ 5- 5- 6 --- 5- 6 81 : 5 5- 7 --- 8+ 5- 6 5- 5- 6 --- --- 5- 8+ 5- 5- 6 --- 6 7 100 : 5 6- 9+ --- 9+ 6- 8 6- 6- 8 --- --- 6- 8 6- 6- 9+ --- 6- 8 121 : 5 7 9 --- 10 7 11+ 7 8 11+ --- --- 6- 11+ 7 6- 11+ --- 7 9 144 : 6 8 10 --- 11 7- 10 9 9 12+ --- --- 8 11 8 7- 12+ --- 7- 10 169 : 7 9 11 --- 12+ 9 11 9 9 12+ --- --- 9 10 9 8- 11 --- 9 11 196 : 8 10 12 --- 13+ 10 13+ 10 10 13+ --- --- 9- 13+ 9- 9- 13+ --- 11 12 225 : 9 10- 13 --- 14 12 14 12 12 15+ --- --- 11 15+ 11 11 15+ --- 12 13 256 : 9 12- 14 --- 15 12- 256+ 13 14 13 --- --- 12- 16 12- 12- 14 --- 13 14 289 : 9 12- 16 --- 16 13 289+ 16 14 16 --- --- 12- 15 13 13 15 --- 14 15 324 : 9 14 15 --- 17 14 324+ 15 15 18 --- --- 13- 17 14 14 17 --- 15 16 361 : 10 14- 17 --- 18 16 21+ 15 16 18 --- --- 15 17 15 15 19 --- 16 17 400 : 11 16 20 --- 19 16 400+ 19 18 20 --- --- 14- 20 16 16 18 --- 17 18 441 : 11 16- 21 --- 20 17 22 20 25 33+ --- --- 16- 20 17 17 21 --- 20 19 484 : 12 18- 20 --- 21 19 23 21 21 24 --- --- 18- 24 18- 19 27+ --- 20 20 529 : 12 20 22 --- 22 20 529+ 20 25 25 --- --- 18- 21 20 18- 24 --- 23 21 576 : 13 21 21 --- 23 20- 576+ 25 22 25 --- --- 21 26 20- 22 26 --- 23 22 625 : 13 21- 25 --- 24 22 625+ 26 25 23 --- --- 21- 29 22 23 25 --- 27 23 676 : 14 24 28 --- 25 25 --- 27 26 25 --- --- 22- 29+ 24 23 26 --- 25 24 729 : 14 24 27 --- 26 25 --- 26 31+ 31+ --- --- 25 29 25 23- 27 --- 24 25 784 : 15 26 29 --- 27 25- --- 32 36+ 28 --- --- 25- 32 26 26 31 --- 27 26 841 : 15 26- 27 --- 28 27 --- 28 29+ 29+ --- --- 26- 29+ 28 28 29+ --- 28 27 900 : 15 28- 30 --- 29 28- --- 31 35 33 --- --- 28- 38+ 29 28- 32 --- 32 Rank 1: Student 13 with score 113 Rank 2: Student 2 with score 120 ===================================== Rank 3: Student 16 with score 122 Rank 4: Student 15 with score 127 Rank 5: Student 6 with score 128 Rank 6: Student 19 with score 155 Rank 7: Student 8 with score 165 Rank 8: Student 3 with score 178 Rank 9: Student 5 with score 182 Rank 10: Student 9 with score 184 Rank 11: Student 17 with score 207 Rank 12: Student 10 with score 216 Rank 13: Student 14 with score 219 Rank 14: Student 7 with score 6917 Rank 15: Student 18 with score 9423 Rank 16: Student 4 with score 9425 Rank 17: Student 11 with score 9441 Rank 17: Student 12 with score 9441