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