Graph forms
for C4 [ 288, 109 ] = UG(ATD[288,134])
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On this page are computer-accessible forms for the graph C4[ 288, 109 ] =
UG(ATD[288,134]).
(I) Following is a form readable by MAGMA:
g:=Graph<288|{ {20, 21}, {209, 211}, {1, 2}, {229, 230}, {109, 110}, {149, 150},
{1, 5}, {3, 7}, {2, 6}, {177, 181}, {243, 246}, {66, 68}, {242, 244}, {225,
231}, {67, 69}, {162, 165}, {233, 238}, {198, 207}, {278, 287}, {85, 94}, {276,
287}, {275, 280}, {115, 120}, {4, 8}, {3, 14}, {231, 234}, {16, 30}, {16, 31},
{192, 208}, {3, 18}, {239, 254}, {15, 30}, {13, 28}, {11, 26}, {9, 24}, {7, 22},
{5, 20}, {106, 123}, {9, 27}, {237, 255}, {224, 242}, {15, 29}, {134, 148},
{170, 184}, {2, 17}, {226, 241}, {10, 25}, {6, 21}, {238, 250}, {262, 274},
{169, 188}, {207, 218}, {4, 19}, {12, 27}, {195, 219}, {205, 213}, {239, 245},
{227, 248}, {67, 94}, {138, 151}, {106, 116}, {206, 208}, {8, 23}, {232, 247},
{104, 119}, {88, 120}, {218, 248}, {89, 125}, {223, 251}, {130, 166}, {144,
180}, {10, 47}, {145, 180}, {131, 165}, {153, 191}, {9, 46}, {95, 120}, {85,
114}, {12, 43}, {222, 246}, {137, 160}, {71, 109}, {135, 172}, {221, 246}, {86,
122}, {211, 253}, {11, 36}, {68, 107}, {13, 61}, {219, 235}, {15, 63}, {14, 62},
{6, 55}, {10, 59}, {8, 57}, {142, 191}, {5, 54}, {9, 58}, {78, 122}, {203, 255},
{151, 163}, {277, 288}, {134, 176}, {11, 60}, {210, 229}, {201, 254}, {198,
241}, {91, 108}, {141, 186}, {13, 52}, {70, 127}, {69, 126}, {219, 224}, {213,
238}, {12, 48}, {21, 41}, {7, 56}, {132, 196}, {137, 201}, {35, 97}, {135, 197},
{144, 210}, {155, 222}, {131, 197}, {185, 255}, {132, 194}, {159, 217}, {128,
199}, {131, 196}, {53, 125}, {32, 105}, {185, 240}, {130, 203}, {4, 78}, {184,
242}, {58, 112}, {45, 103}, {41, 99}, {149, 223}, {129, 202}, {183, 252}, {37,
104}, {182, 251}, {187, 245}, {37, 106}, {38, 105}, {3, 83}, {52, 100}, {19,
67}, {18, 66}, {17, 65}, {16, 64}, {22, 68}, {26, 72}, {23, 69}, {30, 77}, {186,
233}, {31, 75}, {190, 234}, {1, 84}, {31, 74}, {28, 73}, {155, 206}, {48, 102},
{150, 192}, {29, 74}, {169, 243}, {176, 234}, {189, 230}, {58, 102}, {139, 215},
{40, 117}, {42, 119}, {24, 70}, {39, 121}, {25, 71}, {154, 196}, {44, 115}, {33,
65}, {128, 224}, {136, 235}, {21, 113}, {60, 88}, {55, 83}, {14, 107}, {163,
198}, {142, 232}, {34, 69}, {41, 65}, {53, 93}, {50, 90}, {49, 89}, {35, 73},
{29, 118}, {33, 74}, {32, 76}, {58, 86}, {40, 68}, {35, 79}, {34, 78}, {33, 77},
{149, 249}, {178, 222}, {161, 204}, {52, 90}, {53, 91}, {178, 220}, {51, 92},
{141, 226}, {143, 255}, {189, 205}, {147, 227}, {144, 225}, {23, 101}, {140,
254}, {47, 92}, {146, 225}, {178, 193}, {51, 71}, {57, 77}, {32, 85}, {45, 88},
{39, 82}, {37, 80}, {168, 221}, {174, 219}, {47, 89}, {49, 71}, {48, 70}, {138,
252}, {139, 253}, {38, 81}, {145, 230}, {154, 237}, {40, 83}, {188, 199}, {52,
79}, {50, 73}, {44, 87}, {42, 81}, {166, 221}, {171, 208}, {39, 91}, {41, 84},
{43, 86}, {169, 212}, {132, 250}, {133, 251}, {42, 85}, {129, 254}, {1, 129},
{95, 223}, {4, 134}, {34, 160}, {126, 253}, {117, 241}, {118, 242}, {119, 243},
{97, 228}, {124, 249}, {126, 248}, {127, 249}, {125, 247}, {98, 238}, {99, 239},
{121, 244}, {123, 246}, {30, 144}, {88, 215}, {94, 209}, {122, 245}, {82, 194},
{79, 222}, {23, 133}, {28, 143}, {65, 210}, {100, 240}, {24, 142}, {47, 185},
{25, 143}, {10, 157}, {27, 140}, {17, 137}, {92, 196}, {20, 140}, {19, 139},
{18, 138}, {57, 160}, {59, 161}, {81, 203}, {22, 141}, {72, 211}, {56, 164},
{62, 162}, {26, 135}, {62, 163}, {26, 132}, {60, 162}, {31, 128}, {86, 201},
{96, 192}, {111, 207}, {18, 179}, {76, 237}, {32, 130}, {5, 161}, {124, 216},
{13, 168}, {107, 205}, {36, 131}, {75, 236}, {66, 229}, {56, 159}, {15, 167},
{103, 207}, {96, 200}, {112, 216}, {48, 153}, {55, 158}, {50, 155}, {49, 154},
{74, 225}, {72, 227}, {64, 235}, {54, 157}, {106, 193}, {101, 201}, {102, 202},
{124, 208}, {16, 189}, {51, 156}, {104, 199}, {112, 223}, {33, 145}, {80, 224},
{34, 146}, {11, 186}, {38, 148}, {22, 163}, {108, 217}, {2, 180}, {49, 135},
{46, 152}, {12, 187}, {46, 153}, {36, 147}, {116, 195}, {127, 200}, {110, 214},
{111, 215}, {29, 164}, {108, 213}, {44, 150}, {45, 151}, {121, 195}, {123, 192},
{127, 195}, {105, 212}, {113, 204}, {115, 206}, {124, 193}, {43, 149}, {120,
198}, {61, 130}, {63, 128}, {125, 194}, {100, 166}, {99, 160}, {51, 247}, {115,
182}, {117, 179}, {121, 191}, {98, 170}, {116, 188}, {119, 190}, {84, 158},
{111, 165}, {112, 187}, {118, 189}, {103, 171}, {109, 161}, {61, 243}, {82,
156}, {45, 226}, {101, 181}, {103, 182}, {7, 213}, {97, 179}, {96, 178}, {55,
229}, {54, 228}, {59, 232}, {91, 136}, {40, 252}, {108, 184}, {109, 185}, {63,
234}, {111, 186}, {46, 249}, {105, 190}, {99, 180}, {62, 233}, {36, 253}, {96,
188}, {56, 230}, {101, 187}, {57, 231}, {35, 252}, {61, 220}, {114, 147}, {79,
173}, {93, 191}, {64, 164}, {76, 168}, {60, 218}, {114, 148}, {90, 179}, {98,
136}, {14, 226}, {75, 167}, {113, 157}, {116, 152}, {37, 200}, {90, 183}, {72,
165}, {66, 175}, {44, 193}, {94, 176}, {95, 177}, {73, 166}, {19, 227}, {92,
172}, {113, 129}, {93, 174}, {110, 157}, {95, 171}, {107, 159}, {75, 190}, {38,
209}, {93, 170}, {80, 167}, {64, 184}, {82, 170}, {126, 134}, {80, 169}, {81,
168}, {87, 173}, {78, 181}, {84, 175}, {87, 171}, {98, 159}, {118, 136}, {97,
158}, {122, 133}, {6, 263}, {28, 280}, {20, 284}, {8, 258}, {25, 276}, {27,
267}, {17, 258}, {24, 262}, {39, 262}, {43, 264}, {42, 268}, {54, 280}, {59,
267}, {63, 268}, {50, 261}, {53, 269}, {70, 259}, {87, 283}, {67, 273}, {77,
286}, {76, 276}, {89, 260}, {114, 278}, {100, 257}, {102, 256}, {117, 281},
{110, 256}, {83, 288}, {123, 261}, {104, 279}, {155, 283}, {148, 273}, {142,
260}, {153, 274}, {140, 256}, {146, 286}, {154, 278}, {158, 275}, {143, 257},
{151, 281}, {175, 288}, {146, 258}, {138, 283}, {156, 269}, {137, 284}, {150,
259}, {139, 285}, {152, 271}, {133, 285}, {156, 260}, {152, 259}, {141, 272},
{147, 270}, {174, 271}, {172, 270}, {183, 275}, {173, 261}, {174, 262}, {175,
263}, {177, 285}, {167, 266}, {176, 286}, {181, 282}, {183, 263}, {145, 288},
{164, 277}, {162, 272}, {172, 287}, {173, 281}, {177, 264}, {182, 264}, {202,
267}, {212, 279}, {214, 274}, {211, 278}, {200, 271}, {218, 285}, {210, 277},
{197, 269}, {217, 272}, {221, 279}, {194, 265}, {220, 279}, {197, 265}, {199,
266}, {215, 282}, {204, 257}, {216, 264}, {217, 265}, {214, 260}, {203, 287},
{202, 284}, {206, 281}, {205, 277}, {212, 268}, {220, 261}, {216, 259}, {214,
267}, {204, 275}, {209, 270}, {233, 265}, {236, 268}, {235, 266}, {251, 282},
{248, 282}, {228, 263}, {237, 270}, {240, 276}, {228, 257}, {247, 274}, {232,
256}, {240, 280}, {245, 284}, {241, 283}, {250, 272}, {239, 258}, {236, 286},
{231, 273}, {250, 269}, {244, 271}, {236, 273}, {244, 266} }>;
(II) A more general form is to represent the graph as the orbit of {20, 21}
under the group generated by the following permutations:
a: (1, 2, 6, 21, 41, 84)(3, 10, 34, 68, 109, 8)(4, 14, 47, 69, 22, 71)(5, 17,
55, 113, 99, 175)(7, 25, 78, 107, 185, 23)(9, 31, 79, 48, 15, 50)(11, 26, 72,
165, 131, 36)(12, 29, 73, 58, 16, 52)(13, 43, 118, 166, 112, 64)(18, 59, 146,
40, 110, 57)(19, 62, 92, 126, 141, 49)(20, 65, 158, 129, 180, 263)(24, 75, 173,
153, 63, 155)(27, 74, 35, 102, 30, 90)(28, 86, 189, 100, 187, 164)(32, 95, 170,
81, 182, 91)(33, 97, 202, 144, 183, 140)(37, 106, 116, 188, 96, 200)(38, 103,
53, 85, 120, 82)(39, 105, 171, 93, 42, 115)(44, 121, 212, 208, 174, 119)(45,
125, 94, 198, 156, 148)(46, 128, 222, 70, 167, 261)(51, 134, 226, 89, 67,
163)(54, 137, 229, 204, 239, 288)(56, 143, 122, 205, 240, 101)(60, 132, 211,
111, 197, 147)(61, 149, 242, 221, 216, 235)(66, 161, 258, 83, 157, 160)(76, 177,
98, 203, 251, 108)(77, 179, 267, 225, 252, 256)(80, 123, 152, 199, 178, 127)(87,
191, 268, 206, 262, 190)(88, 194, 209, 207, 269, 114)(104, 193, 195, 169, 192,
271)(117, 214, 231, 138, 232, 286)(124, 219, 243, 150, 244, 279)(130, 223, 184,
168, 264, 136)(133, 213, 276, 181, 159, 255)(135, 227, 162, 196, 253, 186)(139,
233, 172, 248, 272, 154)(142, 236, 281, 274, 234, 283)(145, 228, 284, 210, 275,
254)(151, 247, 176, 241, 260, 273)(201, 230, 257, 245, 277, 280)(215, 265, 270,
218, 250, 278)(217, 237, 285, 238, 287, 282)(220, 249, 224, 246, 259, 266) (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, 9)(4, 13)(6, 20)(7, 24)(8, 28)(10, 33)(11, 37)(12, 40)(14, 46)(15,
49)(16, 51)(17, 54)(18, 58)(19, 61)(22, 70)(23, 73)(25, 77)(26, 80)(27, 83)(29,
89)(30, 71)(31, 92)(32, 94)(34, 100)(35, 101)(36, 104)(39, 108)(41, 113)(42,
114)(43, 117)(44, 120)(45, 124)(47, 74)(48, 68)(50, 133)(52, 78)(53, 136)(55,
140)(56, 142)(57, 143)(59, 145)(60, 106)(62, 152)(63, 154)(64, 156)(65, 157)(66,
102)(67, 130)(69, 166)(72, 169)(75, 172)(76, 176)(79, 181)(81, 148)(82, 184)(84,
129)(86, 179)(87, 95)(88, 193)(90, 122)(93, 98)(96, 111)(97, 201)(99, 204)(103,
208)(105, 209)(107, 153)(109, 144)(110, 210)(112, 138)(116, 162)(118, 125)(119,
147)(121, 217)(123, 218)(126, 221)(127, 141)(128, 196)(131, 199)(132, 224)(134,
168)(135, 167)(137, 228)(139, 220)(146, 240)(149, 241)(150, 198)(151, 216)(155,
251)(158, 254)(159, 191)(160, 257)(161, 180)(163, 259)(164, 260)(165, 188)(173,
177)(174, 238)(175, 202)(178, 215)(182, 206)(183, 245)(185, 225)(186, 200)(187,
252)(189, 247)(190, 270)(192, 207)(194, 242)(195, 272)(197, 266)(203, 273)(205,
274)(211, 212)(213, 262)(214, 277)(219, 250)(222, 282)(223, 283)(226, 249)(227,
243)(229, 256)(230, 232)(231, 255)(233, 271)(234, 237)(235, 269)(236, 287)(239,
275)(244, 265)(246, 248)(253, 279)(258, 280)(261, 285)(263, 284)(264, 281)(267,
288)(268, 278)(276, 286)
c: (2, 129)(3, 47)(4, 181)(5, 84)(6, 113)(7, 89)(8, 101)(9, 74)(10, 83)(12,
77)(13, 79)(14, 92)(15, 70)(16, 153)(17, 254)(18, 185)(19, 282)(20, 41)(22,
49)(24, 29)(25, 40)(26, 186)(27, 33)(28, 35)(30, 48)(31, 46)(32, 206)(34,
122)(36, 60)(38, 171)(39, 136)(42, 44)(43, 286)(45, 270)(50, 166)(51, 107)(53,
108)(54, 158)(55, 157)(56, 260)(57, 187)(58, 225)(59, 288)(61, 222)(62, 196)(63,
259)(64, 191)(65, 140)(66, 109)(67, 251)(68, 71)(69, 133)(72, 111)(75, 249)(76,
281)(80, 200)(81, 87)(82, 98)(85, 115)(86, 146)(88, 147)(90, 100)(93, 184)(94,
182)(95, 148)(96, 169)(97, 280)(99, 284)(102, 144)(103, 209)(104, 106)(105,
208)(110, 229)(112, 231)(114, 120)(116, 199)(117, 276)(118, 262)(119, 193)(121,
235)(123, 279)(124, 190)(125, 213)(126, 285)(127, 167)(128, 152)(130, 155)(131,
162)(132, 233)(134, 177)(135, 141)(137, 239)(138, 255)(139, 248)(142, 164)(143,
252)(145, 267)(149, 236)(150, 268)(151, 237)(154, 163)(156, 159)(160, 245)(161,
175)(168, 173)(172, 226)(174, 242)(176, 264)(178, 243)(179, 240)(180, 202)(183,
257)(189, 274)(192, 212)(194, 238)(195, 266)(197, 272)(198, 278)(201, 258)(203,
283)(204, 263)(205, 247)(207, 211)(210, 256)(214, 230)(215, 227)(216, 234)(217,
269)(218, 253)(219, 244)(220, 246)(221, 261)(223, 273)(224, 271)(228, 275)(232,
277)(241, 287)(250, 265)
C4[ 288, 109 ]
288
-1 2 5 84 129
-2 1 180 6 17
-3 14 83 7 18
-4 78 134 8 19
-5 1 161 20 54
-6 55 2 21 263
-7 22 56 3 213
-8 23 57 4 258
-9 24 46 58 27
-10 25 47 157 59
-11 36 26 60 186
-12 187 48 27 43
-13 168 28 61 52
-14 3 226 62 107
-15 167 29 30 63
-16 189 30 31 64
-17 2 137 258 65
-18 66 3 179 138
-19 67 4 139 227
-20 5 140 284 21
-21 113 6 41 20
-22 68 7 141 163
-23 133 101 69 8
-24 70 9 262 142
-25 143 276 71 10
-26 11 132 135 72
-27 12 267 140 9
-28 143 13 280 73
-29 15 74 118 164
-30 77 144 15 16
-31 16 128 74 75
-32 105 85 130 76
-33 77 145 74 65
-34 78 69 146 160
-35 79 73 97 252
-36 11 253 147 131
-37 200 80 104 106
-38 209 81 148 105
-39 121 91 82 262
-40 68 83 117 252
-41 99 84 21 65
-42 81 268 85 119
-43 264 12 149 86
-44 115 193 150 87
-45 88 103 226 151
-46 249 9 152 153
-47 89 92 185 10
-48 12 102 70 153
-49 154 89 135 71
-50 155 90 73 261
-51 156 92 71 247
-52 100 13 79 90
-53 91 125 93 269
-54 157 5 280 228
-55 158 6 83 229
-56 159 7 164 230
-57 77 231 160 8
-58 112 102 9 86
-59 232 267 161 10
-60 11 88 162 218
-61 220 243 13 130
-62 233 14 162 163
-63 234 15 268 128
-64 235 16 184 164
-65 33 210 17 41
-66 68 18 229 175
-67 69 94 19 273
-68 22 66 40 107
-69 23 34 67 126
-70 24 48 127 259
-71 25 49 51 109
-72 165 211 26 227
-73 166 35 28 50
-74 33 225 29 31
-75 167 190 236 31
-76 276 168 237 32
-77 33 286 57 30
-78 34 122 4 181
-79 35 222 52 173
-80 167 37 169 224
-81 168 38 203 42
-82 156 170 39 194
-83 55 288 3 40
-84 1 158 41 175
-85 114 94 42 32
-86 122 58 201 43
-87 44 171 173 283
-88 45 60 215 120
-89 47 125 49 260
-90 179 50 183 52
-91 136 39 53 108
-92 47 51 172 196
-93 191 170 53 174
-94 176 209 67 85
-95 177 223 171 120
-96 188 178 200 192
-97 35 179 158 228
-98 136 159 170 238
-99 180 160 41 239
-100 166 257 52 240
-101 187 23 201 181
-102 58 256 48 202
-103 45 171 182 207
-104 199 37 279 119
-105 190 212 38 32
-106 123 37 116 193
-107 68 14 159 205
-108 91 213 184 217
-109 110 71 161 185
-110 157 256 214 109
-111 165 215 207 186
-112 187 58 223 216
-113 157 204 129 21
-114 278 147 148 85
-115 44 182 206 120
-116 188 106 195 152
-117 179 281 40 241
-118 242 189 136 29
-119 243 190 104 42
-120 88 198 115 95
-121 244 191 39 195
-122 78 133 245 86
-123 246 192 106 261
-124 193 216 249 208
-125 89 247 194 53
-126 253 134 69 248
-127 200 70 249 195
-128 199 224 63 31
-129 1 254 113 202
-130 166 203 61 32
-131 165 36 196 197
-132 26 194 250 196
-133 23 122 251 285
-134 176 4 126 148
-135 26 49 172 197
-136 91 235 118 98
-137 201 17 160 284
-138 18 151 283 252
-139 253 215 19 285
-140 254 256 27 20
-141 22 226 272 186
-142 232 24 191 260
-143 255 25 257 28
-144 210 180 225 30
-145 33 288 180 230
-146 286 34 225 258
-147 36 114 270 227
-148 134 114 38 273
-149 223 150 249 43
-150 44 192 149 259
-151 45 138 281 163
-152 46 116 259 271
-153 46 48 191 274
-154 278 49 237 196
-155 222 50 206 283
-156 82 269 51 260
-157 110 113 10 54
-158 55 275 84 97
-159 56 107 217 98
-160 99 34 57 137
-161 59 5 204 109
-162 165 60 62 272
-163 22 198 62 151
-164 56 277 29 64
-165 111 72 162 131
-166 100 221 73 130
-167 266 80 15 75
-168 221 13 81 76
-169 188 243 80 212
-170 82 93 184 98
-171 103 95 87 208
-172 287 135 92 270
-173 79 281 261 87
-174 93 271 262 219
-175 66 288 84 263
-176 286 134 234 94
-177 264 181 95 285
-178 220 222 193 96
-179 90 18 117 97
-180 99 144 2 145
-181 78 177 101 282
-182 264 103 115 251
-183 275 90 252 263
-184 242 170 64 108
-185 255 47 240 109
-186 11 111 233 141
-187 12 101 112 245
-188 199 169 116 96
-189 16 205 118 230
-190 234 105 75 119
-191 121 93 142 153
-192 123 150 96 208
-193 44 178 124 106
-194 132 265 125 82
-195 121 116 127 219
-196 132 154 92 131
-197 265 135 269 131
-198 163 207 120 241
-199 188 266 104 128
-200 37 127 271 96
-201 254 101 137 86
-202 102 267 129 284
-203 287 255 81 130
-204 275 113 257 161
-205 189 277 213 107
-206 155 115 281 208
-207 198 111 103 218
-208 124 192 171 206
-209 211 38 94 270
-210 144 277 229 65
-211 209 253 278 72
-212 169 268 279 105
-213 7 205 238 108
-214 110 267 260 274
-215 88 111 139 282
-216 264 112 124 259
-217 265 159 272 108
-218 60 248 207 285
-219 224 235 195 174
-220 178 279 61 261
-221 166 168 246 279
-222 155 79 178 246
-223 112 149 95 251
-224 242 80 128 219
-225 231 144 146 74
-226 45 14 141 241
-227 147 72 248 19
-228 257 97 54 263
-229 55 66 210 230
-230 56 145 189 229
-231 57 234 225 273
-232 256 59 247 142
-233 265 62 238 186
-234 176 231 190 63
-235 266 136 64 219
-236 286 268 75 273
-237 154 255 270 76
-238 233 213 250 98
-239 99 254 245 258
-240 100 276 280 185
-241 198 226 117 283
-242 244 224 118 184
-243 169 246 61 119
-244 121 242 266 271
-245 187 122 239 284
-246 221 243 123 222
-247 232 125 51 274
-248 126 227 282 218
-249 46 124 127 149
-250 132 269 238 272
-251 133 223 182 282
-252 35 138 40 183
-253 211 36 126 139
-254 201 129 140 239
-255 143 203 237 185
-256 110 232 102 140
-257 143 100 204 228
-258 146 17 8 239
-259 70 150 216 152
-260 89 156 214 142
-261 220 123 50 173
-262 24 39 174 274
-263 6 183 228 175
-264 177 182 216 43
-265 233 194 217 197
-266 199 167 244 235
-267 59 202 27 214
-268 212 236 63 42
-269 156 250 53 197
-270 209 147 237 172
-271 200 244 152 174
-272 162 217 250 141
-273 231 67 148 236
-274 214 247 262 153
-275 158 280 204 183
-276 287 25 240 76
-277 210 288 205 164
-278 154 287 211 114
-279 220 221 212 104
-280 275 28 240 54
-281 117 151 173 206
-282 181 215 248 251
-283 155 138 87 241
-284 245 202 137 20
-285 133 177 139 218
-286 77 176 146 236
-287 276 278 203 172
-288 145 277 83 175
0