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