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