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