Graph forms
for C4 [ 320, 85 ] = UG(ATD[320,31])
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On this page are computer-accessible forms for the graph C4[ 320, 85 ] =
UG(ATD[320,31]).
(I) Following is a form readable by MAGMA:
g:=Graph<320|{ {84, 85}, {312, 313}, {302, 303}, {226, 227}, {108, 109}, {160,
162}, {228, 230}, {1, 2}, {227, 231}, {1, 4}, {2, 7}, {1, 6}, {35, 43}, {289,
297}, {128, 136}, {292, 301}, {3, 8}, {4, 15}, {119, 124}, {1, 13}, {307, 319},
{5, 9}, {3, 14}, {17, 31}, {34, 44}, {291, 300}, {131, 147}, {132, 148}, {99,
114}, {232, 249}, {104, 121}, {4, 22}, {97, 115}, {12, 30}, {9, 27}, {8, 26},
{5, 23}, {66, 81}, {163, 176}, {5, 16}, {298, 319}, {105, 124}, {131, 150}, {2,
20}, {288, 310}, {238, 248}, {11, 29}, {10, 28}, {3, 21}, {165, 179}, {193,
214}, {64, 88}, {298, 306}, {226, 250}, {71, 95}, {170, 179}, {32, 58}, {303,
309}, {297, 307}, {293, 319}, {268, 278}, {43, 49}, {64, 91}, {65, 90}, {106,
113}, {172, 183}, {106, 118}, {296, 308}, {267, 279}, {262, 282}, {141, 144},
{167, 186}, {171, 182}, {6, 24}, {7, 25}, {164, 187}, {228, 251}, {140, 172},
{203, 235}, {19, 50}, {280, 313}, {257, 288}, {74, 107}, {155, 186}, {82, 112},
{286, 316}, {212, 247}, {152, 189}, {281, 316}, {70, 96}, {256, 294}, {207,
233}, {16, 55}, {271, 296}, {26, 61}, {67, 107}, {285, 309}, {17, 56}, {267,
290}, {197, 236}, {80, 121}, {133, 175}, {284, 310}, {216, 242}, {4, 47}, {65,
106}, {18, 57}, {134, 173}, {81, 125}, {271, 291}, {263, 299}, {3, 46}, {270,
291}, {2, 45}, {264, 295}, {10, 58}, {72, 120}, {196, 245}, {18, 32}, {268,
318}, {19, 33}, {156, 174}, {259, 304}, {265, 314}, {5, 48}, {285, 296}, {204,
249}, {195, 246}, {17, 36}, {78, 120}, {152, 174}, {199, 240}, {272, 295}, {16,
40}, {279, 303}, {11, 50}, {15, 54}, {13, 52}, {30, 36}, {262, 316}, {10, 49},
{14, 53}, {128, 187}, {263, 315}, {27, 38}, {276, 297}, {258, 319}, {130, 188},
{272, 302}, {256, 318}, {12, 51}, {198, 249}, {140, 179}, {55, 119}, {57, 121},
{7, 70}, {189, 252}, {13, 76}, {11, 74}, {9, 72}, {15, 77}, {56, 122}, {6, 69},
{183, 244}, {10, 73}, {168, 235}, {20, 80}, {23, 83}, {22, 82}, {21, 81}, {171,
239}, {29, 88}, {53, 112}, {169, 236}, {21, 83}, {46, 104}, {31, 89}, {12, 75},
{170, 237}, {40, 96}, {46, 102}, {42, 98}, {41, 97}, {149, 221}, {59, 114},
{161, 235}, {28, 87}, {129, 202}, {173, 230}, {24, 84}, {26, 86}, {25, 85}, {14,
67}, {269, 320}, {164, 233}, {167, 234}, {53, 123}, {8, 71}, {177, 254}, {60,
115}, {59, 116}, {44, 99}, {146, 221}, {44, 125}, {11, 89}, {168, 250}, {24,
75}, {37, 118}, {173, 254}, {183, 227}, {62, 104}, {63, 105}, {175, 248}, {41,
112}, {281, 320}, {128, 217}, {172, 245}, {60, 102}, {61, 103}, {166, 252},
{167, 253}, {137, 210}, {180, 239}, {18, 78}, {189, 225}, {45, 113}, {19, 79},
{56, 101}, {143, 210}, {58, 100}, {59, 101}, {166, 248}, {167, 249}, {35, 124},
{175, 240}, {184, 218}, {12, 111}, {181, 214}, {178, 209}, {54, 85}, {139, 239},
{159, 251}, {59, 94}, {130, 231}, {57, 95}, {129, 230}, {178, 213}, {137, 238},
{33, 73}, {149, 253}, {177, 217}, {171, 194}, {34, 72}, {177, 219}, {141, 231},
{183, 220}, {42, 70}, {157, 241}, {158, 242}, {135, 232}, {174, 193}, {169,
216}, {130, 246}, {23, 98}, {151, 225}, {162, 212}, {21, 109}, {56, 64}, {39,
95}, {38, 94}, {37, 93}, {36, 92}, {176, 201}, {20, 110}, {314, 320}, {62, 68},
{33, 91}, {32, 90}, {128, 251}, {160, 222}, {87, 215}, {117, 245}, {13, 140},
{95, 222}, {37, 164}, {19, 146}, {17, 144}, {15, 142}, {8, 138}, {9, 139}, {120,
250}, {14, 141}, {80, 211}, {18, 145}, {111, 236}, {49, 181}, {92, 216}, {51,
182}, {83, 214}, {81, 212}, {111, 233}, {82, 213}, {99, 228}, {118, 254}, {28,
149}, {97, 232}, {73, 192}, {68, 206}, {86, 220}, {69, 207}, {126, 244}, {64,
203}, {94, 210}, {6, 136}, {67, 205}, {66, 204}, {43, 165}, {7, 137}, {121,
247}, {55, 166}, {110, 255}, {50, 161}, {20, 129}, {53, 160}, {117, 224}, {39,
190}, {120, 225}, {62, 164}, {75, 209}, {74, 208}, {119, 237}, {126, 228}, {127,
229}, {89, 194}, {34, 191}, {52, 169}, {114, 239}, {60, 162}, {61, 163}, {124,
226}, {125, 227}, {16, 143}, {77, 210}, {33, 190}, {60, 156}, {26, 187}, {29,
188}, {118, 212}, {25, 186}, {30, 189}, {127, 218}, {61, 155}, {67, 229}, {27,
188}, {35, 139}, {79, 231}, {78, 230}, {63, 151}, {99, 201}, {52, 159}, {107,
192}, {116, 223}, {24, 180}, {98, 206}, {48, 156}, {51, 158}, {22, 184}, {23,
185}, {106, 196}, {41, 134}, {50, 157}, {114, 221}, {37, 149}, {39, 151}, {38,
150}, {34, 147}, {71, 246}, {69, 244}, {42, 152}, {43, 153}, {122, 200}, {70,
245}, {91, 232}, {89, 234}, {104, 219}, {47, 155}, {94, 234}, {123, 207}, {100,
209}, {101, 208}, {44, 154}, {69, 243}, {113, 199}, {119, 193}, {35, 148}, {103,
208}, {107, 220}, {93, 229}, {29, 166}, {31, 163}, {100, 216}, {57, 132}, {100,
217}, {98, 223}, {101, 218}, {68, 134}, {115, 176}, {93, 153}, {52, 241}, {127,
186}, {79, 136}, {32, 233}, {85, 159}, {123, 177}, {25, 213}, {108, 163}, {90,
138}, {58, 235}, {111, 190}, {87, 132}, {66, 150}, {74, 158}, {65, 151}, {75,
157}, {105, 191}, {76, 148}, {42, 247}, {91, 133}, {123, 155}, {45, 204}, {78,
175}, {72, 170}, {36, 192}, {65, 165}, {54, 211}, {102, 131}, {38, 193}, {122,
157}, {82, 187}, {108, 133}, {110, 135}, {40, 194}, {47, 197}, {46, 196}, {109,
134}, {51, 223}, {88, 180}, {45, 195}, {96, 142}, {126, 142}, {54, 199}, {88,
169}, {40, 218}, {125, 143}, {86, 162}, {63, 202}, {80, 165}, {113, 132}, {48,
198}, {96, 150}, {73, 191}, {49, 198}, {62, 201}, {105, 145}, {41, 208}, {87,
170}, {39, 217}, {55, 200}, {22, 274}, {30, 276}, {31, 277}, {28, 275}, {27,
271}, {48, 278}, {47, 260}, {63, 273}, {97, 290}, {92, 280}, {93, 283}, {103,
289}, {92, 283}, {71, 267}, {103, 308}, {66, 279}, {84, 258}, {83, 266}, {68,
280}, {109, 304}, {79, 303}, {76, 302}, {112, 277}, {77, 298}, {110, 261}, {126,
277}, {117, 283}, {90, 309}, {116, 283}, {86, 294}, {76, 318}, {77, 312}, {108,
281}, {116, 257}, {122, 271}, {117, 258}, {115, 266}, {102, 282}, {84, 299},
{127, 256}, {185, 312}, {188, 318}, {135, 260}, {147, 272}, {161, 290}, {182,
306}, {185, 317}, {184, 316}, {145, 276}, {138, 268}, {198, 320}, {153, 287},
{176, 311}, {129, 265}, {139, 261}, {181, 315}, {178, 317}, {191, 304}, {144,
259}, {143, 282}, {160, 309}, {148, 258}, {159, 264}, {174, 313}, {133, 285},
{179, 299}, {135, 286}, {146, 264}, {173, 310}, {184, 292}, {158, 259}, {131,
284}, {145, 270}, {147, 307}, {190, 287}, {182, 275}, {138, 300}, {137, 289},
{130, 299}, {154, 305}, {168, 259}, {156, 304}, {171, 280}, {152, 300}, {153,
301}, {181, 256}, {144, 294}, {146, 292}, {154, 301}, {185, 270}, {168, 287},
{161, 281}, {172, 276}, {136, 305}, {142, 308}, {154, 288}, {180, 265}, {140,
306}, {178, 268}, {141, 307}, {215, 278}, {252, 317}, {221, 284}, {211, 279},
{225, 293}, {243, 310}, {224, 294}, {255, 313}, {207, 264}, {214, 286}, {255,
311}, {252, 308}, {219, 275}, {215, 287}, {215, 286}, {254, 311}, {192, 266},
{206, 260}, {205, 263}, {220, 272}, {253, 305}, {238, 291}, {200, 263}, {244,
293}, {246, 295}, {243, 289}, {251, 297}, {209, 260}, {211, 262}, {229, 306},
{242, 293}, {201, 273}, {213, 269}, {195, 282}, {205, 278}, {247, 298}, {195,
285}, {205, 274}, {236, 269}, {240, 273}, {194, 288}, {243, 273}, {202, 296},
{222, 317}, {237, 265}, {222, 315}, {200, 302}, {202, 290}, {223, 311}, {204,
292}, {197, 300}, {203, 295}, {237, 257}, {241, 257}, {250, 266}, {224, 274},
{255, 269}, {224, 275}, {248, 267}, {206, 314}, {241, 261}, {240, 261}, {219,
301}, {234, 274}, {203, 305}, {238, 277}, {253, 262}, {196, 312}, {242, 270},
{199, 314}, {197, 315}, {226, 284} }>;
(II) A more general form is to represent the graph as the orbit of {84, 85}
under the group generated by the following permutations:
a: (1, 2, 7, 25, 85, 54, 15, 4)(3, 11, 39, 119, 162, 56, 32, 9)(5, 14, 50, 151,
193, 86, 64, 18)(6, 20, 70, 186, 159, 199, 77, 22)(8, 29, 95, 55, 160, 122, 90,
27)(10, 34, 109, 158, 287, 226, 115, 36)(12, 43, 131, 163, 216, 87, 125, 41)(13,
45, 137, 213, 84, 211, 142, 47)(16, 53, 157, 65, 38, 26, 88, 57)(17, 58, 72, 21,
74, 190, 124, 60)(19, 63, 174, 294, 203, 78, 23, 67)(24, 80, 96, 155, 52, 113,
210, 82)(28, 44, 134, 51, 153, 284, 176, 92)(30, 49, 147, 108, 242, 215, 227,
97)(31, 100, 170, 81, 208, 111, 35, 102)(33, 105, 156, 144, 235, 120, 83,
107)(37, 114, 62, 171, 219, 288, 254, 116)(40, 123, 241, 106, 94, 187, 180,
121)(42, 127, 264, 240, 312, 274, 136, 129)(46, 89, 217, 237, 212, 101, 233,
139)(48, 141, 161, 225, 214, 220, 91, 145)(59, 164, 239, 104, 194, 177, 257,
118)(61, 169, 132, 143, 112, 75, 165, 150)(66, 103, 236, 148, 282, 277, 209,
179)(68, 182, 301, 310, 311, 283, 149, 99)(69, 110, 245, 167, 251, 314, 298,
184)(71, 166, 222, 200, 309, 271, 138, 188)(73, 191, 304, 259, 168, 250, 266,
192)(76, 195, 238, 178, 299, 279, 308, 197)(79, 202, 152, 256, 295, 175, 185,
205)(93, 221, 201, 280, 275, 154, 173, 223)(98, 229, 146, 273, 313, 224, 305,
230)(117, 253, 228, 206, 306, 292, 243, 255)(126, 260, 140, 204, 289, 269, 258,
262)(128, 265, 247, 218, 207, 261, 196, 234)(130, 267, 252, 315, 302, 285, 291,
268)(133, 270, 278, 231, 290, 189, 181, 272)(135, 172, 249, 297, 320, 319, 316,
244)(183, 232, 276, 198, 307, 281, 293, 286)(246, 248, 317, 263, 303, 296, 300,
318) (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, 6)(3, 10)(4, 13)(5, 17)(7, 24)(8, 28)(9, 31)(11, 38)(12, 42)(14, 49)(15,
52)(16, 56)(18, 62)(19, 66)(20, 69)(21, 73)(22, 76)(23, 36)(25, 84)(26, 87)(27,
89)(29, 94)(30, 98)(32, 104)(33, 81)(34, 108)(35, 112)(37, 95)(39, 118)(40,
122)(41, 124)(43, 53)(44, 133)(45, 136)(46, 58)(47, 140)(48, 144)(50, 150)(51,
152)(54, 159)(55, 101)(57, 164)(59, 166)(60, 168)(61, 170)(63, 173)(64, 143)(65,
177)(67, 181)(68, 145)(70, 75)(71, 149)(72, 163)(74, 193)(77, 169)(78, 201)(79,
204)(80, 207)(82, 148)(83, 192)(86, 215)(88, 210)(90, 219)(91, 125)(92, 185)(93,
222)(96, 157)(97, 226)(99, 175)(100, 196)(102, 235)(103, 237)(105, 134)(106,
217)(107, 214)(109, 191)(110, 244)(111, 247)(113, 128)(114, 248)(115, 250)(116,
252)(117, 178)(119, 208)(120, 176)(121, 233)(123, 165)(126, 261)(127, 263)(129,
243)(130, 167)(131, 161)(132, 187)(135, 183)(137, 180)(138, 275)(139, 277)(141,
198)(142, 241)(146, 279)(147, 281)(151, 254)(153, 160)(154, 285)(155, 179)(156,
259)(158, 174)(162, 287)(171, 291)(172, 260)(182, 300)(184, 302)(186, 299)(188,
234)(189, 223)(190, 212)(194, 271)(195, 305)(197, 306)(199, 251)(200, 218)(202,
310)(203, 282)(205, 256)(206, 276)(209, 245)(211, 264)(213, 258)(216, 312)(220,
286)(221, 267)(224, 268)(225, 311)(227, 232)(228, 240)(229, 315)(230, 273)(231,
249)(236, 298)(238, 239)(242, 313)(246, 253)(255, 293)(257, 308)(262, 295)(265,
289)(269, 319)(270, 280)(272, 316)(274, 318)(278, 294)(283, 317)(284, 290)(288,
296)(292, 303)(297, 314)(301, 309)(307, 320)
C4[ 320, 85 ]
320
-1 2 13 4 6
-2 1 45 7 20
-3 46 14 8 21
-4 22 1 47 15
-5 23 48 16 9
-6 1 24 69 136
-7 2 25 70 137
-8 3 26 71 138
-9 5 27 72 139
-10 58 49 28 73
-11 89 50 29 74
-12 111 51 30 75
-13 1 52 140 76
-14 67 3 53 141
-15 77 4 54 142
-16 55 143 5 40
-17 56 144 36 31
-18 78 57 145 32
-19 33 79 146 50
-20 110 2 80 129
-21 3 81 83 109
-22 4 82 184 274
-23 5 83 185 98
-24 180 6 84 75
-25 213 7 85 186
-26 187 61 8 86
-27 188 38 271 9
-28 275 149 10 87
-29 11 88 166 188
-30 12 276 189 36
-31 89 277 17 163
-32 90 233 58 18
-33 91 190 73 19
-34 44 147 191 72
-35 124 148 139 43
-36 92 192 17 30
-37 93 149 118 164
-38 27 94 193 150
-39 190 95 151 217
-40 16 194 96 218
-41 112 134 97 208
-42 70 247 152 98
-43 165 35 49 153
-44 99 154 34 125
-45 2 113 204 195
-46 3 102 104 196
-47 155 4 260 197
-48 198 156 278 5
-49 198 181 10 43
-50 11 157 161 19
-51 12 223 158 182
-52 13 169 159 241
-53 112 123 14 160
-54 199 211 15 85
-55 166 200 16 119
-56 122 101 17 64
-57 121 132 18 95
-58 100 235 10 32
-59 101 114 94 116
-60 156 102 115 162
-61 155 26 103 163
-62 68 201 104 164
-63 202 105 151 273
-64 88 56 91 203
-65 165 90 106 151
-66 81 279 204 150
-67 14 205 107 229
-68 134 280 62 206
-69 243 244 6 207
-70 245 7 96 42
-71 267 246 95 8
-72 34 170 9 120
-73 33 191 192 10
-74 11 158 107 208
-75 209 12 24 157
-76 13 148 302 318
-77 210 298 15 312
-78 18 120 175 230
-79 231 136 303 19
-80 121 165 211 20
-81 66 212 125 21
-82 22 187 112 213
-83 23 266 214 21
-84 24 299 258 85
-85 25 159 84 54
-86 220 26 162 294
-87 132 170 28 215
-88 169 180 29 64
-89 11 234 194 31
-90 309 138 32 65
-91 33 133 232 64
-92 36 280 216 283
-93 37 283 229 153
-94 210 234 59 38
-95 57 222 71 39
-96 70 40 150 142
-97 232 290 115 41
-98 23 223 206 42
-99 44 201 114 228
-100 209 58 216 217
-101 56 59 218 208
-102 46 60 282 131
-103 308 289 61 208
-104 121 46 62 219
-105 145 124 191 63
-106 113 118 196 65
-107 220 67 192 74
-108 133 281 163 109
-109 134 304 108 21
-110 255 135 261 20
-111 12 233 190 236
-112 277 82 41 53
-113 132 45 199 106
-114 99 221 59 239
-115 176 266 60 97
-116 223 59 257 283
-117 245 224 258 283
-118 254 212 37 106
-119 55 124 193 237
-120 78 225 72 250
-121 57 80 104 247
-122 56 200 157 271
-123 155 177 53 207
-124 35 105 226 119
-125 44 143 81 227
-126 244 277 228 142
-127 256 218 229 186
-128 187 136 217 251
-129 265 202 20 230
-130 231 188 299 246
-131 102 147 150 284
-132 57 113 148 87
-133 91 108 175 285
-134 68 41 173 109
-135 110 286 232 260
-136 79 6 128 305
-137 210 289 7 238
-138 90 300 268 8
-139 35 239 261 9
-140 13 179 172 306
-141 231 144 14 307
-142 308 15 126 96
-143 210 125 16 282
-144 17 259 294 141
-145 276 105 270 18
-146 264 221 292 19
-147 34 272 131 307
-148 132 35 258 76
-149 253 221 37 28
-150 66 38 96 131
-151 225 39 63 65
-152 189 300 42 174
-153 287 301 93 43
-154 44 288 301 305
-155 123 47 61 186
-156 48 60 304 174
-157 122 50 75 241
-158 242 259 51 74
-159 264 52 85 251
-160 309 222 162 53
-161 235 290 50 281
-162 212 60 160 86
-163 176 61 31 108
-164 187 233 37 62
-165 80 179 43 65
-166 55 248 29 252
-167 253 234 249 186
-168 287 235 259 250
-169 88 236 216 52
-170 179 72 237 87
-171 280 182 194 239
-172 276 245 183 140
-173 254 134 310 230
-174 156 313 193 152
-175 78 133 248 240
-176 201 311 115 163
-177 254 123 217 219
-178 209 213 268 317
-179 165 299 170 140
-180 88 265 24 239
-181 256 49 214 315
-182 275 171 51 306
-183 220 244 172 227
-184 22 292 316 218
-185 23 312 270 317
-186 155 167 25 127
-187 26 82 128 164
-188 27 29 130 318
-189 225 30 152 252
-190 33 111 287 39
-191 34 105 73 304
-192 266 36 73 107
-193 38 214 119 174
-194 89 288 171 40
-195 45 246 282 285
-196 46 245 312 106
-197 47 300 236 315
-198 320 48 49 249
-199 113 314 240 54
-200 55 122 302 263
-201 99 176 62 273
-202 290 63 129 296
-203 235 305 64 295
-204 66 45 292 249
-205 67 278 263 274
-206 68 314 260 98
-207 264 123 233 69
-208 101 103 41 74
-209 100 178 260 75
-210 77 143 137 94
-211 80 279 262 54
-212 81 247 118 162
-213 178 25 82 269
-214 286 181 83 193
-215 286 287 278 87
-216 242 100 92 169
-217 100 177 39 128
-218 101 127 40 184
-219 275 177 301 104
-220 183 107 272 86
-221 146 114 149 284
-222 160 95 315 317
-223 311 116 51 98
-224 275 117 294 274
-225 189 293 151 120
-226 124 227 250 284
-227 231 125 226 183
-228 99 126 251 230
-229 67 93 127 306
-230 78 129 173 228
-231 79 227 130 141
-232 91 135 249 97
-233 111 207 32 164
-234 89 167 94 274
-235 58 168 203 161
-236 111 169 269 197
-237 265 257 170 119
-238 277 137 291 248
-239 114 180 171 139
-240 199 261 273 175
-241 157 257 52 261
-242 158 270 216 293
-243 310 69 289 273
-244 69 126 183 293
-245 70 117 172 196
-246 71 195 130 295
-247 121 298 212 42
-248 166 267 238 175
-249 198 232 167 204
-250 266 168 226 120
-251 297 159 128 228
-252 308 166 189 317
-253 167 149 305 262
-254 177 311 118 173
-255 110 311 269 313
-256 181 127 294 318
-257 288 116 237 241
-258 319 148 84 117
-259 144 168 158 304
-260 209 47 135 206
-261 110 139 240 241
-262 253 211 282 316
-263 200 299 205 315
-264 146 159 207 295
-265 180 237 314 129
-266 115 192 83 250
-267 279 290 71 248
-268 178 278 138 318
-269 320 255 213 236
-270 242 145 291 185
-271 122 27 291 296
-272 220 147 302 295
-273 243 201 63 240
-274 22 234 224 205
-275 224 28 182 219
-276 297 145 172 30
-277 112 126 238 31
-278 48 268 215 205
-279 66 211 267 303
-280 68 92 313 171
-281 320 161 316 108
-282 143 102 195 262
-283 92 93 116 117
-284 221 310 226 131
-285 133 309 195 296
-286 135 214 215 316
-287 168 190 215 153
-288 154 310 257 194
-289 297 243 103 137
-290 267 202 161 97
-291 300 270 238 271
-292 146 301 204 184
-293 242 319 244 225
-294 144 256 224 86
-295 264 246 203 272
-296 308 202 271 285
-297 276 289 251 307
-298 77 319 247 306
-299 179 84 130 263
-300 291 138 152 197
-301 154 292 153 219
-302 200 303 272 76
-303 309 79 279 302
-304 156 191 259 109
-305 154 253 136 203
-306 298 182 140 229
-307 297 319 147 141
-308 103 142 252 296
-309 90 160 303 285
-310 243 288 173 284
-311 176 254 255 223
-312 77 313 185 196
-313 255 312 280 174
-314 199 265 320 206
-315 222 181 197 263
-316 286 281 184 262
-317 178 222 185 252
-318 188 256 268 76
-319 298 258 293 307
-320 198 269 281 314
0