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