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