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