Graph forms
for C4 [ 256, 64 ] = UG(ATD[256,106])
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On this page are computer-accessible forms for the graph C4[ 256, 64 ] =
UG(ATD[256,106]).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {70, 71}, {130, 131}, {144, 145}, {28, 30}, {108, 110}, {1, 2},
{176, 179}, {80, 83}, {73, 74}, {45, 46}, {81, 85}, {194, 198}, {82, 86}, {162,
166}, {2, 7}, {225, 228}, {120, 125}, {152, 158}, {240, 246}, {216, 222}, {185,
191}, {184, 190}, {153, 159}, {1, 6}, {90, 93}, {89, 94}, {75, 76}, {57, 62},
{11, 12}, {121, 126}, {129, 134}, {53, 61}, {229, 237}, {36, 45}, {241, 248},
{131, 137}, {241, 251}, {215, 221}, {3, 8}, {183, 188}, {119, 124}, {151, 156},
{240, 252}, {2, 15}, {214, 219}, {4, 9}, {118, 123}, {247, 249}, {5, 10}, {87,
88}, {101, 117}, {207, 223}, {102, 118}, {34, 51}, {239, 254}, {238, 255}, {236,
253}, {167, 182}, {99, 114}, {42, 59}, {135, 150}, {13, 31}, {199, 213}, {175,
189}, {3, 16}, {14, 29}, {11, 24}, {7, 20}, {4, 17}, {69, 80}, {14, 27}, {12,
25}, {6, 19}, {99, 117}, {227, 245}, {225, 247}, {224, 246}, {5, 18}, {76, 91},
{13, 26}, {32, 56}, {196, 220}, {39, 63}, {33, 57}, {132, 157}, {227, 250},
{226, 248}, {41, 50}, {239, 244}, {108, 119}, {139, 151}, {8, 21}, {238, 243},
{226, 255}, {203, 214}, {10, 23}, {111, 114}, {224, 254}, {236, 242}, {9, 22},
{192, 223}, {168, 183}, {96, 127}, {72, 87}, {35, 60}, {146, 178}, {156, 188},
{157, 189}, {158, 190}, {159, 191}, {64, 97}, {195, 226}, {193, 224}, {128,
161}, {130, 163}, {133, 164}, {148, 181}, {149, 180}, {147, 177}, {223, 253},
{222, 252}, {213, 247}, {205, 239}, {204, 238}, {65, 98}, {211, 240}, {206,
237}, {194, 225}, {129, 162}, {6, 34}, {7, 35}, {31, 58}, {212, 241}, {200,
237}, {14, 40}, {221, 251}, {220, 250}, {197, 227}, {23, 49}, {22, 48}, {15,
41}, {88, 127}, {143, 168}, {144, 183}, {68, 108}, {195, 235}, {86, 126}, {85,
125}, {84, 124}, {83, 123}, {134, 174}, {30, 55}, {207, 230}, {192, 233}, {134,
175}, {24, 50}, {223, 245}, {222, 244}, {198, 236}, {28, 54}, {25, 51}, {146,
184}, {147, 185}, {12, 39}, {193, 234}, {72, 99}, {133, 174}, {8, 36}, {95,
115}, {19, 63}, {18, 62}, {17, 61}, {16, 60}, {10, 38}, {9, 37}, {128, 172},
{136, 165}, {196, 233}, {26, 52}, {221, 243}, {220, 242}, {69, 107}, {27, 53},
{148, 186}, {149, 187}, {64, 111}, {214, 249}, {130, 173}, {132, 171}, {143,
160}, {154, 170}, {87, 102}, {217, 232}, {138, 187}, {66, 112}, {216, 234}, {67,
113}, {155, 169}, {74, 121}, {137, 186}, {15, 59}, {71, 115}, {65, 117}, {140,
184}, {141, 185}, {77, 120}, {93, 104}, {79, 122}, {152, 173}, {153, 172}, {69,
114}, {78, 121}, {135, 176}, {66, 122}, {218, 226}, {92, 100}, {82, 106}, {137,
177}, {138, 178}, {139, 179}, {140, 180}, {141, 181}, {142, 182}, {155, 163},
{201, 240}, {217, 224}, {16, 42}, {91, 97}, {21, 47}, {20, 46}, {17, 43}, {76,
119}, {202, 241}, {79, 116}, {154, 161}, {77, 113}, {215, 235}, {208, 236}, {81,
109}, {29, 32}, {218, 231}, {210, 239}, {75, 118}, {142, 179}, {18, 44}, {89,
103}, {78, 112}, {74, 116}, {31, 33}, {19, 45}, {136, 182}, {145, 175}, {71,
120}, {209, 238}, {35, 96}, {135, 196}, {47, 107}, {167, 227}, {39, 97}, {42,
99}, {47, 102}, {45, 100}, {41, 98}, {46, 101}, {20, 68}, {63, 110}, {151, 198},
{59, 105}, {183, 228}, {20, 64}, {57, 109}, {23, 67}, {22, 66}, {21, 65}, {150,
194}, {144, 197}, {157, 200}, {159, 202}, {30, 72}, {48, 103}, {191, 232}, {182,
225}, {158, 201}, {49, 104}, {190, 231}, {188, 229}, {51, 105}, {55, 108}, {189,
230}, {156, 199}, {24, 68}, {27, 71}, {26, 70}, {25, 69}, {54, 107}, {53, 106},
{63, 96}, {60, 92}, {163, 195}, {160, 192}, {161, 193}, {162, 194}, {165, 196},
{191, 222}, {189, 220}, {177, 211}, {34, 65}, {190, 221}, {43, 79}, {175, 203},
{164, 192}, {48, 85}, {180, 209}, {58, 95}, {56, 93}, {50, 87}, {176, 214},
{178, 212}, {177, 215}, {40, 79}, {188, 219}, {181, 210}, {58, 93}, {57, 94},
{49, 86}, {35, 75}, {166, 206}, {38, 78}, {37, 77}, {36, 76}, {32, 73}, {166,
207}, {178, 216}, {33, 74}, {165, 206}, {55, 92}, {51, 88}, {160, 203}, {164,
200}, {52, 89}, {180, 217}, {54, 91}, {161, 204}, {163, 205}, {171, 197}, {53,
90}, {181, 218}, {59, 84}, {186, 202}, {40, 89}, {169, 216}, {187, 201}, {44,
95}, {173, 217}, {56, 77}, {185, 204}, {184, 205}, {172, 218}, {37, 82}, {49,
70}, {38, 81}, {168, 208}, {187, 195}, {170, 210}, {169, 209}, {41, 80}, {173,
212}, {48, 73}, {43, 81}, {52, 78}, {47, 84}, {186, 193}, {174, 213}, {62, 66},
{179, 207}, {46, 83}, {170, 215}, {44, 82}, {174, 208}, {171, 213}, {61, 67},
{172, 211}, {107, 248}, {91, 243}, {13, 167}, {29, 176}, {68, 246}, {72, 251},
{73, 245}, {67, 131}, {4, 197}, {101, 164}, {11, 202}, {4, 198}, {64, 132}, {50,
244}, {55, 255}, {60, 244}, {56, 242}, {111, 165}, {5, 206}, {1, 205}, {62,
242}, {10, 199}, {5, 203}, {75, 133}, {28, 210}, {3, 204}, {118, 166}, {34,
243}, {1, 211}, {40, 250}, {88, 139}, {94, 141}, {83, 135}, {124, 168}, {125,
169}, {126, 170}, {127, 171}, {28, 201}, {29, 200}, {80, 134}, {90, 140}, {3,
212}, {117, 162}, {33, 249}, {44, 245}, {11, 209}, {90, 128}, {36, 254}, {38,
253}, {39, 252}, {37, 249}, {95, 131}, {94, 130}, {86, 138}, {85, 137}, {84,
136}, {42, 246}, {123, 167}, {13, 208}, {92, 129}, {54, 232}, {58, 229}, {127,
160}, {97, 129}, {115, 146}, {124, 157}, {126, 159}, {125, 158}, {112, 148},
{113, 149}, {27, 253}, {98, 132}, {61, 219}, {12, 235}, {32, 199}, {25, 254},
{116, 147}, {123, 156}, {96, 136}, {112, 152}, {113, 153}, {21, 252}, {115,
154}, {2, 232}, {100, 142}, {14, 228}, {19, 248}, {100, 143}, {6, 234}, {98,
142}, {105, 133}, {23, 250}, {8, 231}, {52, 219}, {9, 230}, {116, 155}, {15,
255}, {104, 152}, {122, 138}, {106, 155}, {22, 229}, {30, 234}, {101, 144},
{103, 146}, {120, 141}, {121, 140}, {18, 228}, {31, 233}, {102, 145}, {109,
154}, {17, 233}, {109, 149}, {110, 150}, {111, 151}, {122, 128}, {16, 235},
{104, 147}, {7, 251}, {26, 230}, {119, 139}, {114, 143}, {103, 153}, {106, 148},
{24, 231}, {105, 150}, {110, 145}, {43, 256}, {70, 256}, {237, 256}, {247, 256}
}>;
(II) A more general form is to represent the graph as the orbit of {70, 71}
under the group generated by the following permutations:
a: (1, 2)(3, 8)(4, 10)(5, 9)(6, 232)(7, 211)(11, 12)(13, 14)(15, 205)(16,
231)(17, 199)(18, 230)(19, 191)(20, 177)(21, 212)(22, 206)(23, 197)(24, 235)(25,
209)(26, 228)(27, 208)(28, 30)(29, 31)(32, 233)(33, 176)(34, 217)(35, 172)(36,
204)(37, 203)(38, 198)(39, 202)(40, 167)(41, 163)(42, 190)(43, 156)(44, 189)(45,
185)(46, 147)(47, 178)(48, 165)(49, 144)(50, 195)(51, 180)(52, 225)(53, 174)(54,
234)(55, 210)(56, 192)(57, 179)(58, 200)(59, 184)(60, 218)(61, 213)(62, 207)(63,
159)(64, 137)(65, 173)(66, 166)(67, 171)(68, 215)(69, 169)(70, 183)(71, 168)(72,
201)(73, 196)(74, 135)(75, 128)(76, 161)(77, 160)(78, 194)(79, 123)(80, 155)(81,
151)(82, 175)(83, 116)(84, 146)(85, 111)(86, 145)(87, 187)(88, 149)(89, 182)(90,
133)(91, 193)(92, 181)(93, 164)(94, 142)(95, 157)(96, 153)(97, 186)(98, 130)(99,
158)(100, 141)(101, 104)(102, 138)(103, 136)(105, 140)(106, 134)(107, 216)(108,
170)(109, 139)(110, 126)(112, 162)(113, 127)(114, 125)(115, 124)(117, 152)(118,
122)(119, 154)(120, 143)(121, 150)(129, 148)(131, 132)(188, 256)(214, 249)(219,
247)(220, 245)(221, 246)(222, 248)(223, 242)(224, 243)(226, 244)(227, 250)(229,
237)(236, 253)(238, 254)(239, 255)(240, 251)(241, 252) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 6)(3, 11)(4, 13)(7, 19)(8, 24)(9, 26)(10, 18)(12, 16)(14, 32)(15, 34)(17,
31)(20, 45)(21, 50)(22, 52)(23, 44)(25, 42)(27, 56)(30, 54)(33, 43)(35, 63)(36,
68)(37, 70)(38, 62)(39, 60)(40, 73)(41, 65)(47, 87)(48, 89)(49, 82)(51, 59)(53,
93)(55, 91)(57, 81)(58, 61)(64, 100)(66, 78)(67, 95)(69, 99)(71, 77)(72,
107)(74, 79)(75, 110)(76, 108)(80, 117)(83, 101)(84, 88)(85, 94)(92, 97)(104,
106)(111, 143)(113, 115)(118, 145)(121, 122)(123, 144)(124, 139)(125, 141)(126,
138)(127, 136)(128, 140)(130, 137)(132, 142)(133, 150)(134, 162)(135, 164)(146,
153)(147, 155)(148, 152)(149, 154)(151, 168)(156, 183)(157, 179)(158, 181)(159,
178)(160, 165)(161, 180)(163, 177)(166, 175)(167, 197)(169, 185)(170, 187)(171,
182)(172, 184)(173, 186)(174, 194)(176, 200)(189, 207)(190, 218)(191, 216)(192,
196)(193, 217)(195, 215)(198, 208)(199, 228)(201, 210)(202, 212)(203, 206)(204,
209)(205, 211)(213, 225)(214, 237)(219, 229)(220, 223)(221, 226)(232, 234)(239,
240)(242, 253)(243, 255)(244, 252)(245, 250)(246, 254)(248, 251)(249, 256)
c: (2, 205)(6, 211)(7, 163)(8, 204)(9, 198)(10, 203)(12, 202)(14, 200)(15,
184)(16, 212)(17, 197)(18, 206)(19, 177)(20, 155)(21, 161)(22, 194)(23, 160)(24,
209)(25, 159)(26, 208)(27, 157)(30, 201)(31, 167)(32, 176)(33, 123)(34, 172)(35,
130)(36, 185)(37, 151)(38, 175)(39, 186)(40, 164)(41, 140)(42, 178)(43, 144)(44,
165)(45, 147)(46, 116)(47, 154)(48, 150)(49, 143)(50, 180)(51, 153)(52, 174)(53,
132)(54, 210)(55, 158)(56, 179)(57, 118)(58, 182)(59, 146)(60, 173)(61, 171)(62,
166)(63, 137)(64, 106)(65, 128)(66, 162)(67, 127)(68, 169)(69, 126)(70, 168)(71,
124)(72, 187)(73, 135)(74, 83)(75, 94)(76, 141)(77, 139)(78, 134)(79, 101)(80,
121)(81, 145)(82, 111)(84, 115)(85, 110)(86, 114)(87, 149)(88, 113)(89, 133)(90,
98)(91, 181)(92, 152)(93, 142)(95, 136)(96, 131)(97, 148)(99, 138)(100,
104)(102, 109)(103, 105)(107, 170)(108, 125)(112, 129)(117, 122)(119, 120)(156,
249)(183, 256)(188, 247)(189, 253)(190, 255)(191, 254)(192, 250)(193, 252)(195,
251)(196, 245)(199, 214)(207, 242)(213, 219)(215, 248)(216, 246)(217, 244)(218,
243)(220, 223)(221, 226)(222, 224)(225, 229)(227, 233)(228, 237)(230, 236)(231,
238)(232, 239)(234, 240)(235, 241)
C4[ 256, 64 ]
256
-1 2 211 6 205
-2 1 232 15 7
-3 212 16 204 8
-4 198 17 9 197
-5 203 18 206 10
-6 1 34 234 19
-7 2 35 20 251
-8 231 3 36 21
-9 22 4 37 230
-10 23 199 5 38
-11 209 12 24 202
-12 11 25 235 39
-13 167 26 31 208
-14 27 29 40 228
-15 2 255 59 41
-16 3 235 60 42
-17 233 4 61 43
-18 44 5 62 228
-19 45 6 248 63
-20 46 68 7 64
-21 47 8 65 252
-22 66 48 9 229
-23 67 49 250 10
-24 11 231 68 50
-25 12 254 69 51
-26 13 70 52 230
-27 253 14 71 53
-28 210 201 30 54
-29 176 200 14 32
-30 55 234 28 72
-31 33 13 233 58
-32 56 199 29 73
-33 57 249 74 31
-34 243 6 51 65
-35 60 7 96 75
-36 45 254 8 76
-37 77 82 249 9
-38 253 78 81 10
-39 12 63 97 252
-40 89 79 14 250
-41 80 15 50 98
-42 99 59 246 16
-43 79 256 81 17
-44 245 82 18 95
-45 100 46 36 19
-46 45 101 83 20
-47 102 84 107 21
-48 22 103 73 85
-49 23 70 104 86
-50 24 244 41 87
-51 88 34 25 105
-52 78 89 26 219
-53 90 27 61 106
-54 232 91 28 107
-55 255 92 30 108
-56 77 242 93 32
-57 33 94 62 109
-58 93 95 31 229
-59 15 105 84 42
-60 35 244 92 16
-61 67 17 53 219
-62 66 242 57 18
-63 110 39 19 96
-64 132 111 20 97
-65 34 117 21 98
-66 22 122 112 62
-67 23 113 61 131
-68 24 246 20 108
-69 25 80 114 107
-70 256 26 49 71
-71 70 27 115 120
-72 99 30 251 87
-73 245 48 74 32
-74 33 121 116 73
-75 133 35 118 76
-76 36 91 75 119
-77 56 113 37 120
-78 121 112 38 52
-79 122 116 40 43
-80 134 69 83 41
-81 38 85 43 109
-82 44 37 106 86
-83 46 123 80 135
-84 47 124 59 136
-85 48 81 125 137
-86 49 82 126 138
-87 88 102 50 72
-88 127 51 139 87
-89 103 94 40 52
-90 93 128 140 53
-91 243 97 54 76
-92 55 100 60 129
-93 56 90 58 104
-94 89 57 130 141
-95 44 58 115 131
-96 35 136 127 63
-97 91 39 129 64
-98 132 41 65 142
-99 114 72 117 42
-100 143 45 92 142
-101 144 46 117 164
-102 145 47 118 87
-103 89 146 48 153
-104 147 49 93 152
-105 133 59 51 150
-106 155 82 148 53
-107 47 69 248 54
-108 55 110 68 119
-109 154 57 81 149
-110 145 150 63 108
-111 165 114 151 64
-112 66 78 148 152
-113 77 67 149 153
-114 99 143 111 69
-115 154 146 71 95
-116 155 79 147 74
-117 99 101 162 65
-118 166 123 102 75
-119 124 139 108 76
-120 77 125 71 141
-121 78 126 74 140
-122 66 79 138 128
-123 156 167 83 118
-124 157 168 84 119
-125 158 169 85 120
-126 121 159 170 86
-127 88 160 171 96
-128 122 90 161 172
-129 134 92 162 97
-130 94 173 163 131
-131 67 137 95 130
-132 157 171 64 98
-133 105 75 174 164
-134 80 129 174 175
-135 176 83 150 196
-136 165 182 84 96
-137 177 85 131 186
-138 187 122 178 86
-139 88 179 151 119
-140 121 90 180 184
-141 181 94 185 120
-142 100 179 182 98
-143 100 168 114 160
-144 101 145 183 197
-145 110 144 102 175
-146 178 103 115 184
-147 177 104 116 185
-148 112 181 106 186
-149 187 113 180 109
-150 110 135 105 194
-151 198 111 156 139
-152 112 158 104 173
-153 113 103 159 172
-154 115 170 161 109
-155 169 116 106 163
-156 188 199 123 151
-157 132 189 200 124
-158 190 201 125 152
-159 191 202 126 153
-160 143 192 203 127
-161 154 193 204 128
-162 166 117 194 129
-163 155 205 195 130
-164 133 101 200 192
-165 111 136 206 196
-166 118 162 206 207
-167 13 123 182 227
-168 143 124 183 208
-169 209 155 125 216
-170 154 210 126 215
-171 132 213 127 197
-172 211 128 218 153
-173 212 217 130 152
-174 133 134 213 208
-175 134 145 189 203
-176 135 179 214 29
-177 211 147 137 215
-178 146 212 138 216
-179 176 139 207 142
-180 209 149 140 217
-181 210 148 141 218
-182 167 136 225 142
-183 144 188 168 228
-184 146 190 205 140
-185 147 191 204 141
-186 202 137 148 193
-187 201 138 149 195
-188 156 183 229 219
-189 220 157 175 230
-190 231 221 158 184
-191 232 222 159 185
-192 233 223 160 164
-193 234 224 161 186
-194 198 225 150 162
-195 187 235 226 163
-196 165 220 233 135
-197 144 4 171 227
-198 4 236 194 151
-199 156 213 10 32
-200 157 237 29 164
-201 187 158 28 240
-202 11 159 186 241
-203 5 214 160 175
-204 3 161 238 185
-205 1 184 239 163
-206 165 166 5 237
-207 166 179 223 230
-208 13 168 236 174
-209 11 169 180 238
-210 170 181 28 239
-211 1 177 172 240
-212 178 3 173 241
-213 199 247 171 174
-214 176 203 249 219
-215 177 221 235 170
-216 178 222 234 169
-217 232 180 224 173
-218 231 181 226 172
-219 188 214 61 52
-220 242 189 250 196
-221 243 190 215 251
-222 244 191 216 252
-223 253 245 192 207
-224 254 246 193 217
-225 247 182 194 228
-226 255 248 195 218
-227 167 245 250 197
-228 14 225 18 183
-229 22 188 58 237
-230 189 26 9 207
-231 24 190 8 218
-232 2 191 217 54
-233 192 17 31 196
-234 6 193 216 30
-235 12 16 215 195
-236 198 242 253 208
-237 200 256 206 229
-238 209 243 255 204
-239 210 254 244 205
-240 211 201 246 252
-241 212 202 248 251
-242 220 56 236 62
-243 34 221 91 238
-244 222 60 50 239
-245 44 223 73 227
-246 68 224 42 240
-247 256 213 225 249
-248 226 19 107 241
-249 33 37 214 247
-250 220 23 40 227
-251 221 72 7 241
-252 222 39 240 21
-253 223 27 38 236
-254 25 36 224 239
-255 55 15 226 238
-256 70 247 237 43
0