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