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