C4graphGraph forms for C4 [ 309, 1 ] = C_309(1,104)

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On this page are computer-accessible forms for the graph C4[ 309, 1 ] = C_309(1,104).

(I) Following is a form readable by MAGMA:

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

(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.

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

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