Graph forms
for C4 [ 257, 1 ] = C_257(1,16)
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On this page are computer-accessible forms for the graph C4[ 257, 1 ] =
C_257(1,16).
(I) Following is a form readable by MAGMA:
g:=Graph<257|{ {2, 3}, {256, 257}, {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}, {224, 225}, {222,
223}, {220, 221}, {218, 219}, {216, 217}, {214, 215}, {212, 213}, {210, 211},
{208, 209}, {206, 207}, {116, 117}, {114, 115}, {112, 113}, {110, 111}, {108,
109}, {106, 107}, {104, 105}, {102, 103}, {100, 101}, {98, 99}, {96, 97}, {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}, {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}, {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}, {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}, {113, 114}, {109, 110}, {105, 106}, {101,
102}, {97, 98}, {93, 94}, {89, 90}, {85, 86}, {81, 82}, {77, 78}, {73, 74}, {69,
70}, {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}, {57, 58}, {61, 62}, {65,
66}, {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}, {197, 198}, {201, 202}, {3, 4}, {251, 252}, {243, 244}, {235, 236},
{227, 228}, {219, 220}, {211, 212}, {115, 116}, {107, 108}, {99, 100}, {91, 92},
{83, 84}, {75, 76}, {67, 68}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44},
{51, 52}, {59, 60}, {123, 124}, {131, 132}, {139, 140}, {147, 148}, {155, 156},
{163, 164}, {171, 172}, {179, 180}, {187, 188}, {195, 196}, {203, 204}, {7, 8},
{247, 248}, {231, 232}, {215, 216}, {103, 104}, {87, 88}, {71, 72}, {23, 24},
{39, 40}, {55, 56}, {119, 120}, {135, 136}, {151, 152}, {167, 168}, {183, 184},
{199, 200}, {1, 17}, {239, 255}, {238, 254}, {237, 253}, {236, 252}, {235, 251},
{234, 250}, {233, 249}, {232, 248}, {231, 247}, {230, 246}, {229, 245}, {228,
244}, {227, 243}, {226, 242}, {225, 241}, {224, 240}, {207, 223}, {206, 222},
{205, 221}, {111, 127}, {110, 126}, {109, 125}, {108, 124}, {107, 123}, {106,
122}, {105, 121}, {104, 120}, {103, 119}, {102, 118}, {101, 117}, {100, 116},
{99, 115}, {98, 114}, {97, 113}, {96, 112}, {79, 95}, {78, 94}, {77, 93}, {76,
92}, {75, 91}, {74, 90}, {73, 89}, {72, 88}, {71, 87}, {70, 86}, {69, 85}, {68,
84}, {67, 83}, {66, 82}, {2, 18}, {3, 19}, {4, 20}, {5, 21}, {6, 22}, {7, 23},
{8, 24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14, 30}, {15, 31},
{32, 48}, {33, 49}, {34, 50}, {35, 51}, {36, 52}, {37, 53}, {38, 54}, {39, 55},
{40, 56}, {41, 57}, {42, 58}, {43, 59}, {44, 60}, {45, 61}, {46, 62}, {47, 63},
{64, 80}, {65, 81}, {128, 144}, {129, 145}, {130, 146}, {131, 147}, {132, 148},
{133, 149}, {134, 150}, {135, 151}, {136, 152}, {137, 153}, {138, 154}, {139,
155}, {140, 156}, {141, 157}, {142, 158}, {143, 159}, {160, 176}, {161, 177},
{162, 178}, {163, 179}, {164, 180}, {165, 181}, {166, 182}, {167, 183}, {168,
184}, {169, 185}, {170, 186}, {171, 187}, {172, 188}, {173, 189}, {174, 190},
{175, 191}, {192, 208}, {193, 209}, {194, 210}, {195, 211}, {196, 212}, {197,
213}, {198, 214}, {199, 215}, {200, 216}, {201, 217}, {202, 218}, {203, 219},
{204, 220}, {15, 16}, {239, 240}, {207, 208}, {111, 112}, {79, 80}, {47, 48},
{143, 144}, {175, 176}, {16, 32}, {223, 239}, {222, 238}, {221, 237}, {220,
236}, {219, 235}, {218, 234}, {217, 233}, {216, 232}, {215, 231}, {214, 230},
{213, 229}, {212, 228}, {211, 227}, {210, 226}, {209, 225}, {208, 224}, {95,
111}, {94, 110}, {93, 109}, {92, 108}, {91, 107}, {90, 106}, {89, 105}, {88,
104}, {87, 103}, {86, 102}, {85, 101}, {84, 100}, {83, 99}, {82, 98}, {81, 97},
{80, 96}, {17, 33}, {18, 34}, {19, 35}, {20, 36}, {21, 37}, {22, 38}, {23, 39},
{24, 40}, {25, 41}, {26, 42}, {27, 43}, {28, 44}, {29, 45}, {30, 46}, {31, 47},
{144, 160}, {145, 161}, {146, 162}, {147, 163}, {148, 164}, {149, 165}, {150,
166}, {151, 167}, {152, 168}, {153, 169}, {154, 170}, {155, 171}, {156, 172},
{157, 173}, {158, 174}, {159, 175}, {31, 32}, {223, 224}, {95, 96}, {159, 160},
{48, 64}, {49, 65}, {50, 66}, {51, 67}, {52, 68}, {53, 69}, {54, 70}, {55, 71},
{56, 72}, {57, 73}, {58, 74}, {59, 75}, {60, 76}, {61, 77}, {62, 78}, {63, 79},
{176, 192}, {177, 193}, {178, 194}, {179, 195}, {180, 196}, {181, 197}, {182,
198}, {183, 199}, {184, 200}, {185, 201}, {186, 202}, {187, 203}, {188, 204},
{189, 205}, {190, 206}, {191, 207}, {63, 64}, {191, 192}, {112, 128}, {115,
131}, {114, 130}, {113, 129}, {116, 132}, {117, 133}, {118, 134}, {119, 135},
{120, 136}, {121, 137}, {122, 138}, {123, 139}, {124, 140}, {125, 141}, {126,
142}, {127, 143}, {2, 243}, {4, 245}, {6, 247}, {8, 249}, {10, 251}, {12, 253},
{14, 255}, {1, 242}, {5, 246}, {9, 250}, {13, 254}, {3, 244}, {11, 252}, {7,
248}, {127, 128}, {1, 257}, {15, 256}, {16, 257}, {240, 256}, {241, 257}, {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, 17, 257, 242)(3, 33, 256, 226)(4, 49, 255, 210)(5, 65, 254, 194)(6, 81,
253, 178)(7, 97, 252, 162)(8, 113, 251, 146)(9, 129, 250, 130)(10, 145, 249,
114)(11, 161, 248, 98)(12, 177, 247, 82)(13, 193, 246, 66)(14, 209, 245, 50)(15,
225, 244, 34)(16, 241, 243, 18)(19, 32, 240, 227)(20, 48, 239, 211)(21, 64, 238,
195)(22, 80, 237, 179)(23, 96, 236, 163)(24, 112, 235, 147)(25, 128, 234,
131)(26, 144, 233, 115)(27, 160, 232, 99)(28, 176, 231, 83)(29, 192, 230,
67)(30, 208, 229, 51)(31, 224, 228, 35)(36, 47, 223, 212)(37, 63, 222, 196)(38,
79, 221, 180)(39, 95, 220, 164)(40, 111, 219, 148)(41, 127, 218, 132)(42, 143,
217, 116)(43, 159, 216, 100)(44, 175, 215, 84)(45, 191, 214, 68)(46, 207, 213,
52)(53, 62, 206, 197)(54, 78, 205, 181)(55, 94, 204, 165)(56, 110, 203, 149)(57,
126, 202, 133)(58, 142, 201, 117)(59, 158, 200, 101)(60, 174, 199, 85)(61, 190,
198, 69)(70, 77, 189, 182)(71, 93, 188, 166)(72, 109, 187, 150)(73, 125, 186,
134)(74, 141, 185, 118)(75, 157, 184, 102)(76, 173, 183, 86)(87, 92, 172,
167)(88, 108, 171, 151)(89, 124, 170, 135)(90, 140, 169, 119)(91, 156, 168,
103)(104, 107, 155, 152)(105, 123, 154, 136)(106, 139, 153, 120)(121, 122, 138,
137) (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, 257)
C4[ 257, 1 ]
257
-1 242 2 257 17
-2 1 243 3 18
-3 2 244 4 19
-4 3 245 5 20
-5 4 246 6 21
-6 22 5 247 7
-7 23 6 248 8
-8 24 7 249 9
-9 25 8 250 10
-10 11 26 9 251
-11 12 27 10 252
-12 11 253 13 28
-13 12 254 14 29
-14 13 255 15 30
-15 14 256 16 31
-16 15 257 17 32
-17 33 1 16 18
-18 34 2 17 19
-19 35 3 18 20
-20 36 4 19 21
-21 22 37 5 20
-22 23 38 6 21
-23 22 24 39 7
-24 23 25 40 8
-25 24 26 41 9
-26 25 27 42 10
-27 11 26 28 43
-28 44 12 27 29
-29 45 13 28 30
-30 46 14 29 31
-31 47 15 30 32
-32 33 48 16 31
-33 34 49 17 32
-34 33 35 50 18
-35 34 36 51 19
-36 35 37 52 20
-37 36 38 53 21
-38 22 37 39 54
-39 55 23 38 40
-40 56 24 39 41
-41 57 25 40 42
-42 58 26 41 43
-43 44 59 27 42
-44 45 60 28 43
-45 44 46 61 29
-46 45 47 62 30
-47 46 48 63 31
-48 47 49 64 32
-49 33 48 50 65
-50 66 34 49 51
-51 67 35 50 52
-52 68 36 51 53
-53 69 37 52 54
-54 55 70 38 53
-55 56 71 39 54
-56 55 57 72 40
-57 56 58 73 41
-58 57 59 74 42
-59 58 60 75 43
-60 44 59 61 76
-61 77 45 60 62
-62 78 46 61 63
-63 79 47 62 64
-64 80 48 63 65
-65 66 81 49 64
-66 67 82 50 65
-67 66 68 83 51
-68 67 69 84 52
-69 68 70 85 53
-70 69 71 86 54
-71 55 70 72 87
-72 88 56 71 73
-73 89 57 72 74
-74 90 58 73 75
-75 91 59 74 76
-76 77 92 60 75
-77 78 93 61 76
-78 77 79 94 62
-79 78 80 95 63
-80 79 81 96 64
-81 80 82 97 65
-82 66 81 83 98
-83 99 67 82 84
-84 100 68 83 85
-85 101 69 84 86
-86 102 70 85 87
-87 88 103 71 86
-88 89 104 72 87
-89 88 90 105 73
-90 89 91 106 74
-91 90 92 107 75
-92 91 93 108 76
-93 77 92 94 109
-94 110 78 93 95
-95 111 79 94 96
-96 112 80 95 97
-97 113 81 96 98
-98 99 114 82 97
-99 100 115 83 98
-100 99 101 116 84
-101 100 102 117 85
-102 101 103 118 86
-103 102 104 119 87
-104 88 103 105 120
-105 121 89 104 106
-106 122 90 105 107
-107 123 91 106 108
-108 124 92 107 109
-109 110 125 93 108
-110 111 126 94 109
-111 110 112 127 95
-112 111 113 128 96
-113 112 114 129 97
-114 113 115 130 98
-115 99 114 116 131
-116 132 100 115 117
-117 133 101 116 118
-118 134 102 117 119
-119 135 103 118 120
-120 121 136 104 119
-121 122 137 105 120
-122 121 123 138 106
-123 122 124 139 107
-124 123 125 140 108
-125 124 126 141 109
-126 110 125 127 142
-127 143 111 126 128
-128 144 112 127 129
-129 145 113 128 130
-130 146 114 129 131
-131 132 147 115 130
-132 133 148 116 131
-133 132 134 149 117
-134 133 135 150 118
-135 134 136 151 119
-136 135 137 152 120
-137 121 136 138 153
-138 154 122 137 139
-139 155 123 138 140
-140 156 124 139 141
-141 157 125 140 142
-142 143 158 126 141
-143 144 159 127 142
-144 143 145 160 128
-145 144 146 161 129
-146 145 147 162 130
-147 146 148 163 131
-148 132 147 149 164
-149 165 133 148 150
-150 166 134 149 151
-151 167 135 150 152
-152 168 136 151 153
-153 154 169 137 152
-154 155 170 138 153
-155 154 156 171 139
-156 155 157 172 140
-157 156 158 173 141
-158 157 159 174 142
-159 143 158 160 175
-160 176 144 159 161
-161 177 145 160 162
-162 178 146 161 163
-163 179 147 162 164
-164 165 180 148 163
-165 166 181 149 164
-166 165 167 182 150
-167 166 168 183 151
-168 167 169 184 152
-169 168 170 185 153
-170 154 169 171 186
-171 187 155 170 172
-172 188 156 171 173
-173 189 157 172 174
-174 190 158 173 175
-175 176 191 159 174
-176 177 192 160 175
-177 176 178 193 161
-178 177 179 194 162
-179 178 180 195 163
-180 179 181 196 164
-181 165 180 182 197
-182 198 166 181 183
-183 199 167 182 184
-184 200 168 183 185
-185 201 169 184 186
-186 187 202 170 185
-187 188 203 171 186
-188 187 189 204 172
-189 188 190 205 173
-190 189 191 206 174
-191 190 192 207 175
-192 176 191 193 208
-193 209 177 192 194
-194 210 178 193 195
-195 211 179 194 196
-196 212 180 195 197
-197 198 213 181 196
-198 199 214 182 197
-199 198 200 215 183
-200 199 201 216 184
-201 200 202 217 185
-202 201 203 218 186
-203 187 202 204 219
-204 220 188 203 205
-205 221 189 204 206
-206 222 190 205 207
-207 223 191 206 208
-208 209 224 192 207
-209 210 225 193 208
-210 209 211 226 194
-211 210 212 227 195
-212 211 213 228 196
-213 212 214 229 197
-214 198 213 215 230
-215 231 199 214 216
-216 232 200 215 217
-217 233 201 216 218
-218 234 202 217 219
-219 220 235 203 218
-220 221 236 204 219
-221 220 222 237 205
-222 221 223 238 206
-223 222 224 239 207
-224 223 225 240 208
-225 209 224 226 241
-226 242 210 225 227
-227 243 211 226 228
-228 244 212 227 229
-229 245 213 228 230
-230 231 246 214 229
-231 232 247 215 230
-232 231 233 248 216
-233 232 234 249 217
-234 233 235 250 218
-235 234 236 251 219
-236 220 235 237 252
-237 253 221 236 238
-238 254 222 237 239
-239 255 223 238 240
-240 256 224 239 241
-241 242 257 225 240
-242 1 243 226 241
-243 242 2 244 227
-244 243 3 245 228
-245 244 4 246 229
-246 245 5 247 230
-247 231 246 6 248
-248 232 247 7 249
-249 233 248 8 250
-250 234 249 9 251
-251 235 250 10 252
-252 11 253 236 251
-253 12 254 237 252
-254 253 13 255 238
-255 254 14 256 239
-256 255 15 257 240
-257 1 256 16 241
0