C4graphGraph forms for C4 [ 512, 123 ] = UG(ATD[512,204])

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On this page are computer-accessible forms for the graph C4[ 512, 123 ] = UG(ATD[512,204]).

(I) Following is a form readable by MAGMA:

g:=Graph<512|{ {42, 43}, {388, 389}, {364, 365}, {342, 343}, {112, 113}, {106, 107}, {266, 267}, {81, 83}, {165, 167}, {1, 2}, {429, 430}, {92, 95}, {48, 52}, {344, 348}, {2, 7}, {320, 325}, {217, 220}, {250, 255}, {217, 223}, {1, 6}, {321, 326}, {82, 85}, {27, 28}, {290, 293}, {129, 137}, {323, 331}, {244, 252}, {114, 123}, {453, 460}, {391, 398}, {389, 396}, {353, 360}, {307, 314}, {117, 124}, {322, 328}, {324, 334}, {3, 8}, {390, 397}, {114, 126}, {4, 9}, {166, 168}, {452, 458}, {5, 10}, {434, 445}, {368, 383}, {71, 72}, {11, 27}, {483, 499}, {34, 50}, {15, 31}, {14, 30}, {13, 29}, {12, 28}, {6, 23}, {456, 473}, {8, 25}, {7, 22}, {197, 212}, {103, 117}, {133, 151}, {5, 22}, {482, 497}, {394, 409}, {173, 190}, {9, 26}, {4, 16}, {236, 248}, {106, 127}, {2, 20}, {480, 502}, {455, 465}, {395, 413}, {3, 21}, {297, 319}, {205, 218}, {488, 511}, {130, 154}, {392, 400}, {141, 149}, {225, 249}, {47, 54}, {485, 508}, {101, 124}, {64, 89}, {140, 150}, {484, 510}, {102, 125}, {486, 509}, {481, 506}, {207, 211}, {487, 507}, {393, 405}, {10, 23}, {195, 222}, {40, 54}, {199, 217}, {7, 24}, {97, 126}, {272, 304}, {471, 503}, {66, 99}, {475, 506}, {466, 499}, {407, 438}, {88, 121}, {201, 232}, {11, 41}, {79, 109}, {17, 51}, {16, 50}, {76, 104}, {77, 105}, {264, 300}, {281, 317}, {477, 504}, {68, 98}, {479, 505}, {412, 442}, {267, 301}, {467, 500}, {12, 36}, {144, 184}, {128, 169}, {449, 488}, {15, 37}, {476, 502}, {320, 363}, {448, 492}, {478, 498}, {157, 176}, {472, 501}, {468, 505}, {349, 371}, {470, 504}, {145, 190}, {474, 501}, {270, 289}, {16, 32}, {147, 163}, {19, 35}, {18, 34}, {17, 33}, {151, 166}, {385, 432}, {275, 288}, {333, 377}, {18, 39}, {8, 62}, {337, 359}, {129, 183}, {88, 110}, {86, 96}, {9, 63}, {271, 313}, {139, 188}, {399, 440}, {258, 309}, {135, 190}, {6, 60}, {348, 358}, {7, 61}, {223, 228}, {25, 37}, {451, 511}, {450, 510}, {384, 444}, {329, 373}, {26, 39}, {463, 498}, {461, 496}, {457, 500}, {65, 124}, {210, 239}, {140, 179}, {462, 497}, {144, 208}, {415, 479}, {410, 474}, {312, 376}, {179, 243}, {170, 234}, {180, 244}, {38, 103}, {393, 456}, {315, 378}, {176, 241}, {136, 201}, {283, 346}, {53, 119}, {434, 496}, {419, 481}, {272, 339}, {411, 472}, {390, 453}, {386, 449}, {284, 351}, {137, 205}, {431, 491}, {422, 482}, {415, 475}, {414, 474}, {413, 473}, {408, 476}, {407, 467}, {406, 466}, {405, 465}, {275, 343}, {282, 350}, {299, 367}, {30, 91}, {423, 482}, {421, 480}, {398, 459}, {318, 379}, {314, 383}, {312, 381}, {171, 238}, {273, 340}, {280, 349}, {282, 351}, {289, 356}, {40, 110}, {306, 372}, {60, 122}, {189, 251}, {256, 326}, {257, 327}, {264, 334}, {265, 335}, {291, 357}, {39, 96}, {422, 481}, {397, 458}, {394, 461}, {160, 231}, {46, 105}, {274, 341}, {284, 347}, {171, 227}, {447, 503}, {406, 478}, {385, 457}, {384, 456}, {310, 382}, {174, 230}, {293, 364}, {429, 484}, {411, 466}, {402, 475}, {10, 64}, {428, 486}, {317, 375}, {128, 202}, {27, 81}, {259, 328}, {438, 509}, {424, 483}, {412, 471}, {263, 332}, {274, 350}, {410, 470}, {409, 469}, {408, 468}, {276, 344}, {277, 345}, {279, 347}, {12, 65}, {305, 380}, {131, 206}, {129, 204}, {37, 104}, {14, 67}, {260, 329}, {262, 331}, {276, 345}, {31, 81}, {425, 487}, {293, 363}, {13, 66}, {426, 485}, {395, 452}, {392, 455}, {304, 383}, {59, 116}, {186, 245}, {261, 330}, {23, 71}, {442, 490}, {427, 507}, {30, 78}, {29, 77}, {28, 76}, {26, 74}, {25, 73}, {24, 72}, {297, 377}, {298, 378}, {299, 379}, {20, 69}, {303, 382}, {161, 240}, {301, 380}, {148, 198}, {430, 508}, {270, 348}, {21, 70}, {444, 495}, {263, 340}, {302, 381}, {55, 99}, {445, 489}, {52, 97}, {446, 491}, {155, 206}, {262, 339}, {153, 207}, {443, 493}, {316, 362}, {191, 233}, {19, 68}, {441, 494}, {401, 454}, {161, 246}, {53, 98}, {148, 204}, {167, 255}, {31, 70}, {146, 203}, {49, 104}, {271, 342}, {277, 332}, {296, 369}, {55, 109}, {437, 495}, {436, 494}, {164, 254}, {130, 217}, {404, 463}, {166, 253}, {163, 248}, {265, 338}, {267, 336}, {273, 330}, {23, 75}, {402, 462}, {401, 461}, {400, 460}, {160, 252}, {138, 214}, {137, 213}, {135, 219}, {58, 102}, {57, 101}, {56, 100}, {24, 68}, {298, 374}, {133, 216}, {433, 492}, {303, 370}, {268, 337}, {294, 376}, {435, 493}, {319, 353}, {59, 100}, {173, 242}, {162, 253}, {269, 338}, {152, 248}, {177, 209}, {150, 247}, {288, 321}, {143, 237}, {175, 205}, {145, 243}, {149, 246}, {138, 238}, {387, 487}, {159, 251}, {158, 250}, {157, 249}, {182, 210}, {63, 90}, {432, 469}, {428, 457}, {172, 201}, {272, 373}, {275, 374}, {35, 69}, {424, 462}, {147, 245}, {146, 244}, {261, 355}, {51, 84}, {439, 464}, {159, 247}, {426, 450}, {134, 239}, {269, 356}, {148, 254}, {427, 449}, {425, 451}, {421, 463}, {417, 459}, {48, 92}, {388, 488}, {62, 82}, {51, 95}, {50, 94}, {49, 93}, {291, 335}, {286, 371}, {391, 489}, {32, 79}, {256, 367}, {280, 375}, {33, 80}, {155, 234}, {257, 368}, {259, 370}, {279, 357}, {420, 470}, {145, 226}, {150, 229}, {258, 369}, {44, 88}, {47, 91}, {46, 90}, {45, 89}, {289, 341}, {38, 83}, {36, 82}, {418, 468}, {305, 327}, {260, 371}, {404, 483}, {278, 353}, {416, 472}, {296, 337}, {403, 490}, {308, 333}, {52, 78}, {423, 477}, {300, 342}, {139, 240}, {420, 479}, {165, 222}, {281, 354}, {285, 358}, {40, 84}, {416, 476}, {43, 87}, {42, 86}, {41, 85}, {185, 197}, {264, 372}, {286, 354}, {287, 355}, {294, 346}, {143, 242}, {419, 478}, {189, 192}, {285, 352}, {414, 480}, {47, 80}, {418, 477}, {316, 323}, {142, 241}, {287, 352}, {62, 191}, {301, 428}, {296, 426}, {297, 427}, {96, 230}, {107, 237}, {84, 211}, {99, 235}, {365, 485}, {26, 144}, {63, 181}, {78, 194}, {28, 145}, {361, 484}, {67, 205}, {29, 146}, {294, 425}, {292, 437}, {319, 429}, {87, 196}, {373, 486}, {91, 200}, {24, 142}, {25, 143}, {21, 140}, {22, 141}, {68, 223}, {64, 222}, {95, 193}, {20, 139}, {113, 238}, {63, 160}, {60, 157}, {62, 159}, {56, 154}, {307, 401}, {58, 152}, {57, 155}, {38, 133}, {368, 467}, {61, 158}, {106, 206}, {127, 219}, {35, 134}, {295, 386}, {109, 203}, {115, 213}, {59, 156}, {71, 224}, {79, 231}, {72, 225}, {377, 464}, {76, 229}, {74, 227}, {108, 198}, {363, 449}, {120, 210}, {302, 388}, {73, 226}, {380, 471}, {311, 412}, {125, 214}, {107, 192}, {77, 230}, {110, 194}, {111, 195}, {108, 193}, {125, 208}, {45, 130}, {75, 228}, {34, 146}, {311, 391}, {310, 390}, {309, 389}, {118, 198}, {94, 238}, {38, 150}, {121, 200}, {313, 392}, {292, 405}, {49, 131}, {369, 451}, {315, 393}, {307, 385}, {306, 384}, {123, 201}, {94, 236}, {50, 128}, {32, 147}, {43, 152}, {101, 209}, {119, 195}, {112, 196}, {33, 148}, {318, 395}, {44, 153}, {35, 149}, {374, 448}, {115, 197}, {108, 218}, {308, 387}, {317, 394}, {80, 232}, {104, 209}, {382, 455}, {313, 384}, {105, 208}, {83, 233}, {380, 454}, {376, 450}, {309, 399}, {110, 212}, {126, 197}, {379, 448}, {87, 235}, {115, 207}, {41, 151}, {379, 453}, {378, 452}, {85, 234}, {120, 199}, {121, 187}, {383, 445}, {374, 436}, {360, 426}, {357, 423}, {356, 422}, {340, 406}, {19, 215}, {378, 446}, {358, 418}, {352, 420}, {100, 161}, {372, 433}, {364, 425}, {355, 422}, {113, 180}, {102, 160}, {381, 443}, {362, 428}, {355, 421}, {345, 415}, {344, 414}, {338, 404}, {122, 188}, {336, 407}, {382, 441}, {341, 402}, {375, 447}, {321, 392}, {327, 398}, {325, 396}, {338, 408}, {381, 439}, {373, 447}, {372, 446}, {369, 443}, {368, 442}, {359, 429}, {343, 413}, {339, 409}, {322, 393}, {326, 397}, {65, 143}, {371, 445}, {370, 444}, {358, 424}, {341, 411}, {340, 410}, {324, 395}, {335, 415}, {342, 390}, {61, 239}, {330, 408}, {74, 152}, {73, 155}, {20, 199}, {97, 178}, {323, 407}, {75, 158}, {106, 191}, {366, 440}, {367, 441}, {75, 156}, {336, 391}, {328, 400}, {346, 386}, {332, 404}, {331, 403}, {330, 402}, {329, 401}, {103, 190}, {335, 406}, {93, 135}, {367, 437}, {97, 187}, {96, 186}, {334, 405}, {102, 186}, {71, 154}, {370, 431}, {98, 188}, {365, 435}, {361, 439}, {60, 220}, {362, 394}, {93, 189}, {70, 166}, {69, 165}, {61, 221}, {57, 216}, {79, 174}, {73, 168}, {66, 163}, {64, 161}, {78, 172}, {343, 437}, {87, 181}, {86, 180}, {83, 177}, {65, 162}, {359, 388}, {354, 385}, {99, 128}, {74, 169}, {32, 196}, {375, 403}, {76, 170}, {95, 185}, {94, 184}, {85, 179}, {84, 178}, {77, 171}, {67, 164}, {109, 138}, {326, 431}, {70, 173}, {361, 386}, {360, 387}, {349, 438}, {332, 423}, {111, 132}, {81, 189}, {91, 183}, {366, 387}, {320, 430}, {56, 215}, {89, 182}, {72, 167}, {121, 136}, {116, 134}, {339, 417}, {111, 156}, {347, 424}, {127, 140}, {69, 176}, {108, 153}, {327, 432}, {376, 399}, {92, 164}, {90, 163}, {345, 416}, {331, 434}, {328, 433}, {100, 157}, {101, 159}, {334, 436}, {123, 129}, {119, 141}, {344, 419}, {357, 414}, {352, 411}, {351, 420}, {350, 421}, {347, 416}, {107, 151}, {351, 419}, {350, 418}, {349, 417}, {118, 136}, {356, 410}, {354, 412}, {333, 435}, {122, 132}, {80, 175}, {93, 162}, {215, 468}, {213, 467}, {215, 474}, {55, 292}, {196, 473}, {58, 292}, {214, 456}, {210, 499}, {199, 502}, {198, 509}, {216, 484}, {135, 440}, {131, 451}, {138, 458}, {206, 396}, {132, 463}, {153, 459}, {132, 472}, {136, 469}, {219, 443}, {36, 325}, {213, 447}, {216, 435}, {3, 366}, {214, 441}, {130, 498}, {219, 427}, {134, 498}, {133, 511}, {57, 440}, {173, 300}, {170, 299}, {154, 283}, {82, 464}, {168, 298}, {142, 268}, {122, 504}, {127, 508}, {174, 301}, {11, 399}, {222, 346}, {181, 304}, {124, 507}, {17, 409}, {224, 360}, {225, 361}, {184, 305}, {227, 362}, {15, 389}, {165, 296}, {220, 337}, {119, 505}, {167, 297}, {144, 286}, {126, 496}, {228, 363}, {13, 413}, {156, 268}, {117, 485}, {48, 417}, {125, 492}, {255, 366}, {46, 444}, {98, 497}, {179, 288}, {114, 486}, {111, 506}, {249, 364}, {147, 260}, {250, 365}, {113, 491}, {120, 482}, {141, 278}, {158, 258}, {42, 436}, {177, 303}, {176, 302}, {18, 397}, {182, 278}, {118, 471}, {13, 431}, {116, 470}, {18, 433}, {185, 282}, {186, 281}, {11, 430}, {105, 460}, {115, 469}, {120, 479}, {188, 283}, {116, 476}, {175, 263}, {174, 262}, {169, 257}, {168, 256}, {142, 294}, {184, 272}, {185, 273}, {170, 259}, {172, 261}, {187, 274}, {164, 270}, {183, 285}, {88, 500}, {89, 501}, {162, 271}, {178, 287}, {66, 492}, {139, 293}, {169, 262}, {171, 260}, {187, 276}, {112, 448}, {172, 284}, {123, 459}, {191, 271}, {241, 320}, {243, 322}, {149, 295}, {67, 496}, {242, 321}, {247, 324}, {90, 494}, {232, 348}, {252, 329}, {92, 490}, {245, 323}, {112, 455}, {14, 438}, {54, 398}, {86, 495}, {177, 264}, {251, 322}, {253, 324}, {4, 446}, {42, 400}, {182, 268}, {183, 269}, {221, 359}, {255, 325}, {178, 265}, {236, 336}, {241, 333}, {175, 274}, {14, 432}, {180, 266}, {181, 267}, {223, 353}, {44, 403}, {202, 266}, {4, 453}, {207, 270}, {247, 310}, {117, 439}, {224, 290}, {233, 299}, {237, 303}, {246, 308}, {248, 314}, {51, 503}, {118, 434}, {245, 305}, {47, 490}, {218, 287}, {221, 283}, {234, 300}, {114, 442}, {244, 316}, {212, 285}, {242, 315}, {59, 497}, {5, 462}, {56, 499}, {29, 465}, {34, 494}, {193, 269}, {218, 279}, {239, 290}, {243, 318}, {224, 302}, {246, 312}, {31, 464}, {49, 510}, {211, 284}, {229, 298}, {240, 319}, {226, 306}, {231, 311}, {58, 491}, {236, 317}, {41, 507}, {202, 280}, {203, 281}, {233, 315}, {192, 275}, {237, 318}, {211, 263}, {225, 309}, {226, 310}, {227, 311}, {33, 500}, {53, 480}, {40, 509}, {193, 276}, {204, 282}, {194, 277}, {235, 316}, {9, 465}, {37, 508}, {200, 273}, {204, 277}, {208, 266}, {5, 478}, {228, 312}, {229, 313}, {230, 314}, {250, 295}, {254, 291}, {200, 279}, {1, 481}, {43, 458}, {195, 290}, {232, 265}, {1, 483}, {194, 289}, {8, 493}, {36, 450}, {53, 466}, {15, 487}, {19, 506}, {30, 503}, {221, 308}, {44, 454}, {46, 452}, {3, 488}, {103, 396}, {21, 510}, {22, 504}, {249, 278}, {45, 477}, {209, 288}, {192, 306}, {240, 258}, {12, 511}, {235, 286}, {27, 493}, {45, 475}, {2, 501}, {212, 291}, {17, 489}, {48, 457}, {202, 307}, {131, 377}, {54, 461}, {55, 460}, {203, 304}, {220, 295}, {251, 256}, {254, 261}, {10, 502}, {252, 257}, {39, 473}, {253, 259}, {6, 505}, {16, 495}, {231, 280}, {52, 512}, {137, 512}, {454, 512}, {489, 512} }>;

(II) A more general form is to represent the graph as the orbit of {42, 43} under the group generated by the following permutations:

a: (2, 6)(3, 11)(7, 23)(8, 27)(9, 16)(10, 22)(12, 37)(13, 42)(14, 17)(15, 36)(19, 56)(20, 60)(21, 41)(24, 71)(25, 28)(26, 50)(29, 86)(30, 51)(31, 82)(32, 63)(33, 67)(34, 39)(35, 100)(38, 106)(40, 52)(43, 66)(44, 114)(45, 53)(46, 112)(47, 92)(48, 54)(49, 124)(55, 58)(57, 135)(59, 134)(61, 75)(62, 81)(64, 141)(65, 104)(68, 154)(69, 157)(70, 85)(73, 145)(74, 128)(76, 143)(77, 180)(78, 84)(79, 160)(80, 164)(83, 191)(87, 163)(88, 126)(89, 119)(90, 196)(91, 95)(93, 101)(94, 144)(96, 146)(97, 110)(98, 130)(99, 152)(102, 109)(103, 206)(105, 113)(107, 150)(108, 129)(111, 210)(115, 136)(117, 131)(118, 213)(120, 132)(121, 197)(122, 199)(123, 153)(125, 138)(127, 133)(137, 198)(139, 220)(140, 151)(142, 224)(147, 181)(148, 205)(149, 161)(155, 190)(156, 239)(159, 189)(162, 209)(165, 249)(166, 179)(167, 225)(168, 243)(170, 242)(171, 266)(172, 211)(173, 234)(174, 252)(175, 254)(177, 271)(178, 194)(182, 195)(183, 193)(185, 200)(186, 203)(187, 212)(188, 217)(192, 247)(201, 207)(202, 227)(204, 218)(208, 238)(216, 219)(221, 228)(222, 278)(223, 283)(229, 237)(230, 244)(232, 270)(235, 248)(236, 286)(240, 295)(241, 302)(245, 304)(250, 258)(253, 288)(255, 309)(256, 322)(257, 262)(259, 321)(260, 267)(261, 263)(264, 342)(265, 289)(268, 290)(272, 305)(274, 291)(275, 324)(276, 285)(277, 287)(279, 282)(280, 311)(293, 337)(294, 360)(296, 364)(297, 361)(298, 318)(299, 315)(301, 329)(303, 313)(306, 310)(307, 362)(308, 312)(314, 316)(317, 354)(319, 386)(320, 388)(323, 383)(325, 389)(326, 328)(327, 339)(330, 340)(331, 368)(332, 355)(333, 381)(334, 343)(335, 341)(336, 371)(338, 356)(344, 358)(345, 352)(346, 353)(347, 351)(349, 391)(350, 357)(359, 363)(365, 369)(366, 399)(367, 393)(370, 392)(372, 390)(373, 380)(374, 395)(375, 412)(376, 387)(377, 439)(378, 379)(382, 384)(385, 394)(397, 433)(398, 417)(400, 431)(401, 428)(402, 406)(403, 442)(404, 422)(405, 437)(407, 445)(408, 410)(409, 432)(411, 415)(413, 436)(414, 418)(416, 420)(419, 424)(421, 423)(425, 426)(427, 484)(429, 449)(430, 488)(434, 467)(435, 443)(438, 489)(441, 456)(444, 455)(446, 453)(447, 471)(448, 452)(450, 487)(451, 485)(454, 486)(457, 461)(458, 492)(460, 491)(462, 478)(463, 482)(465, 495)(466, 475)(468, 474)(470, 476)(472, 479)(473, 494)(477, 480)(481, 483)(496, 500)(497, 498)(499, 506)(501, 505)(502, 504)(507, 510)(508, 511)(509, 512)
b: (2, 483)(3, 118)(6, 481)(7, 424)(8, 471)(9, 453)(10, 478)(11, 213)(12, 486)(13, 42)(14, 216)(15, 44)(16, 446)(17, 219)(19, 468)(20, 404)(21, 434)(22, 462)(23, 419)(24, 358)(25, 380)(26, 390)(27, 447)(28, 373)(29, 400)(30, 435)(31, 403)(32, 378)(33, 427)(34, 433)(35, 408)(36, 114)(37, 454)(38, 349)(39, 397)(40, 451)(41, 467)(43, 413)(45, 53)(46, 112)(47, 377)(48, 117)(49, 461)(50, 372)(51, 443)(52, 485)(54, 131)(55, 405)(56, 474)(57, 432)(58, 437)(59, 470)(60, 422)(61, 347)(62, 412)(63, 379)(64, 406)(65, 428)(66, 436)(67, 484)(68, 418)(69, 338)(70, 331)(71, 344)(72, 348)(73, 305)(74, 342)(75, 351)(76, 329)(77, 392)(78, 365)(79, 315)(80, 297)(81, 375)(82, 442)(83, 280)(84, 369)(85, 368)(86, 431)(87, 395)(88, 487)(89, 466)(90, 448)(91, 333)(92, 439)(93, 394)(94, 306)(95, 381)(96, 326)(97, 426)(98, 477)(99, 334)(100, 410)(101, 385)(102, 367)(103, 417)(104, 401)(105, 455)(106, 391)(107, 336)(108, 388)(109, 393)(110, 425)(111, 479)(113, 444)(115, 399)(119, 475)(120, 132)(121, 387)(122, 482)(123, 325)(124, 457)(125, 441)(126, 450)(127, 489)(128, 264)(129, 320)(130, 480)(133, 438)(134, 476)(135, 409)(136, 366)(137, 430)(138, 456)(139, 332)(140, 445)(141, 402)(142, 285)(143, 301)(144, 310)(145, 272)(146, 328)(147, 298)(148, 449)(149, 330)(150, 371)(151, 407)(152, 343)(153, 389)(154, 414)(155, 327)(156, 420)(157, 356)(158, 284)(159, 354)(160, 299)(161, 340)(162, 362)(163, 374)(164, 361)(165, 265)(166, 323)(167, 232)(168, 245)(169, 300)(170, 252)(171, 313)(172, 250)(173, 262)(174, 242)(175, 319)(176, 269)(177, 202)(178, 296)(179, 383)(180, 370)(181, 318)(182, 411)(183, 241)(184, 226)(185, 312)(186, 256)(187, 360)(188, 423)(189, 317)(190, 339)(191, 311)(192, 236)(193, 302)(194, 364)(195, 415)(196, 452)(197, 376)(198, 488)(199, 463)(200, 308)(201, 255)(203, 322)(204, 363)(205, 429)(206, 398)(207, 309)(208, 382)(209, 307)(210, 472)(211, 258)(212, 294)(217, 421)(218, 359)(220, 355)(221, 279)(222, 335)(223, 350)(224, 276)(225, 270)(227, 271)(228, 282)(229, 260)(230, 321)(231, 233)(234, 257)(235, 324)(237, 267)(238, 384)(239, 416)(240, 263)(243, 304)(244, 259)(246, 273)(247, 286)(248, 275)(249, 289)(251, 281)(253, 316)(254, 386)(261, 295)(266, 303)(268, 352)(274, 353)(277, 293)(278, 341)(283, 357)(287, 337)(288, 314)(290, 345)(291, 346)(396, 459)(440, 469)(458, 473)(460, 465)(464, 490)(491, 495)(492, 494)(493, 503)(496, 510)(497, 504)(498, 502)(499, 501)(500, 507)(505, 506)(508, 512)(509, 511)
c: (1, 2, 501, 89, 45, 130, 498, 134, 116, 59, 497, 98, 53, 119, 505, 6)(3, 51, 493, 30, 11, 67, 507, 126, 117, 123, 396, 153, 131, 88, 510, 33)(4, 16, 495, 86, 42, 43, 458, 138, 214, 125, 492, 66, 13, 29, 465, 9)(5, 19, 502, 111, 120, 122, 499, 22, 215, 10, 506, 199, 132, 210, 504, 56)(7, 474, 64, 475, 217, 463, 239, 470, 100, 462, 68, 480, 195, 479, 60, 483)(8, 503, 27, 14, 41, 496, 124, 114, 103, 459, 206, 44, 49, 500, 21, 17)(12, 509, 133, 54, 57, 490, 135, 48, 127, 512, 37, 213, 31, 469, 82, 118)(15, 115, 464, 136, 36, 198, 511, 40, 216, 47, 440, 92, 219, 52, 508, 137)(18, 55, 473, 105, 112, 90, 491, 34, 292, 39, 460, 196, 46, 113, 494, 58)(20, 472, 182, 477, 154, 478, 35, 476, 156, 482, 188, 466, 141, 468, 23, 481)(24, 414, 222, 415, 220, 404, 61, 410, 161, 402, 223, 421, 290, 420, 157, 424)(25, 447, 81, 432, 85, 434, 65, 486, 38, 398, 155, 403, 93, 457, 140, 489)(26, 453, 32, 444, 180, 436, 152, 397, 109, 456, 208, 448, 163, 431, 146, 405)(28, 438, 151, 461, 101, 442, 190, 417, 106, 454, 104, 467, 70, 409, 62, 471)(50, 437, 96, 400, 87, 452, 238, 441, 102, 433, 99, 413, 77, 455, 63, 446)(69, 416, 268, 423, 283, 406, 149, 408, 75, 422, 139, 411, 278, 418, 71, 419)(72, 344, 165, 345, 337, 332, 221, 340, 246, 330, 228, 355, 293, 352, 249, 358)(73, 375, 189, 385, 179, 445, 143, 373, 83, 327, 234, 331, 162, 428, 150, 391)(74, 390, 79, 384, 266, 374, 248, 326, 203, 393, 144, 379, 147, 370, 244, 334)(76, 407, 166, 394, 159, 412, 145, 349, 107, 401, 209, 368, 173, 339, 191, 380)(78, 430, 205, 487, 197, 439, 201, 325, 108, 451, 110, 484, 80, 366, 95, 443)(84, 435, 91, 399, 164, 427, 97, 485, 129, 389, 207, 377, 121, 450, 148, 488)(94, 367, 186, 328, 235, 395, 171, 382, 160, 372, 128, 343, 230, 392, 181, 378)(142, 357, 346, 335, 295, 338, 158, 356, 240, 341, 353, 350, 224, 351, 176, 347)(167, 276, 296, 277, 359, 263, 308, 273, 312, 261, 363, 287, 364, 285, 225, 348)(168, 317, 251, 354, 243, 371, 237, 329, 177, 257, 300, 262, 271, 301, 229, 336)(169, 342, 174, 313, 267, 298, 236, 256, 281, 322, 286, 318, 260, 303, 252, 264)(170, 323, 253, 362, 247, 311, 226, 280, 192, 307, 288, 383, 242, 272, 233, 305)(172, 320, 218, 425, 212, 361, 232, 255, 193, 369, 194, 429, 175, 387, 185, 381)(178, 365, 183, 309, 270, 297, 187, 426, 204, 388, 211, 333, 200, 376, 254, 449)(184, 299, 245, 259, 316, 324, 227, 310, 231, 306, 202, 275, 314, 321, 304, 315)(241, 279, 294, 291, 386, 265, 250, 269, 258, 289, 319, 274, 360, 282, 302, 284)

(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
C4[ 512, 123 ]
512
-1 2 6 481 483
-2 1 501 7 20
-3 366 488 8 21
-4 453 16 446 9
-5 22 462 478 10
-6 1 23 60 505
-7 22 2 24 61
-8 3 25 62 493
-9 465 4 26 63
-10 23 5 502 64
-11 430 399 27 41
-12 36 511 28 65
-13 66 431 413 29
-14 67 432 30 438
-15 487 37 389 31
-16 495 4 50 32
-17 33 409 489 51
-18 34 397 433 39
-19 506 35 68 215
-20 199 2 69 139
-21 3 70 510 140
-22 5 7 141 504
-23 71 6 75 10
-24 68 72 7 142
-25 143 37 73 8
-26 144 39 74 9
-27 11 81 28 493
-28 12 145 27 76
-29 77 13 146 465
-30 78 14 91 503
-31 464 15 70 81
-32 79 147 16 196
-33 80 148 500 17
-34 146 50 18 494
-35 134 69 149 19
-36 12 82 325 450
-37 508 25 15 104
-38 133 103 83 150
-39 473 26 18 96
-40 110 509 84 54
-41 11 507 85 151
-42 400 436 86 43
-43 458 42 152 87
-44 88 454 403 153
-45 89 475 477 130
-46 452 90 444 105
-47 80 91 490 54
-48 92 457 52 417
-49 510 93 104 131
-50 34 16 94 128
-51 17 84 95 503
-52 78 48 512 97
-53 466 480 119 98
-54 398 47 40 461
-55 99 292 460 109
-56 154 100 499 215
-57 440 155 101 216
-58 102 292 491 152
-59 100 156 497 116
-60 220 122 157 6
-61 221 158 7 239
-62 191 82 159 8
-63 90 181 160 9
-64 89 222 161 10
-65 143 12 124 162
-66 99 13 492 163
-67 496 14 205 164
-68 24 223 19 98
-69 165 176 35 20
-70 166 173 31 21
-71 154 23 224 72
-72 24 167 71 225
-73 155 25 168 226
-74 26 169 227 152
-75 23 156 158 228
-76 104 170 28 229
-77 105 171 29 230
-78 172 194 30 52
-79 231 174 32 109
-80 33 232 47 175
-81 189 27 83 31
-82 464 36 62 85
-83 177 233 81 38
-84 178 211 40 51
-85 179 234 82 41
-86 495 180 96 42
-87 235 181 196 43
-88 44 110 121 500
-89 45 182 501 64
-90 46 63 163 494
-91 200 47 183 30
-92 48 490 95 164
-93 189 135 49 162
-94 236 50 238 184
-95 92 193 51 185
-96 39 86 186 230
-97 187 178 126 52
-98 188 68 497 53
-99 55 66 235 128
-100 56 157 59 161
-101 209 57 124 159
-102 58 125 160 186
-103 396 190 38 117
-104 209 37 49 76
-105 77 46 460 208
-106 191 127 107 206
-107 192 237 106 151
-108 198 193 218 153
-109 55 79 203 138
-110 88 212 40 194
-111 132 506 156 195
-112 113 455 448 196
-113 112 180 238 491
-114 123 442 486 126
-115 213 469 207 197
-116 134 476 59 470
-117 485 124 103 439
-118 198 136 434 471
-119 195 53 141 505
-120 199 210 479 482
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-122 132 188 60 504
-123 201 114 129 459
-124 507 101 117 65
-125 102 214 492 208
-126 496 114 97 197
-127 508 106 140 219
-128 99 169 202 50
-129 123 137 204 183
-130 154 45 498 217
-131 451 377 49 206
-132 111 122 463 472
-133 38 511 216 151
-134 35 498 116 239
-135 440 190 93 219
-136 121 201 469 118
-137 213 512 205 129
-138 214 238 458 109
-139 188 293 20 240
-140 179 127 150 21
-141 22 278 149 119
-142 24 268 294 241
-143 242 25 237 65
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-145 243 190 28 226
-146 34 244 203 29
-147 245 260 163 32
-148 33 198 254 204
-149 35 246 141 295
-150 38 247 140 229
-151 133 166 41 107
-152 58 248 74 43
-153 44 459 108 207
-154 56 71 283 130
-155 57 234 73 206
-156 111 59 268 75
-157 176 100 60 249
-158 258 61 250 75
-159 101 247 62 251
-160 231 102 63 252
-161 100 246 64 240
-162 253 93 271 65
-163 66 90 147 248
-164 67 254 92 270
-165 167 222 69 296
-166 253 168 70 151
-167 165 297 255 72
-168 166 298 256 73
-169 257 128 74 262
-170 299 234 259 76
-171 77 227 238 260
-172 78 201 261 284
-173 242 190 300 70
-174 79 301 262 230
-175 80 205 263 274
-176 69 157 302 241
-177 209 264 83 303
-178 265 287 84 97
-179 243 288 85 140
-180 244 266 113 86
-181 267 304 63 87
-182 89 210 278 268
-183 91 269 129 285
-184 144 94 272 305
-185 95 282 273 197
-186 102 245 281 96
-187 121 276 97 274
-188 122 139 283 98
-189 81 93 192 251
-190 145 135 103 173
-191 233 62 106 271
-192 275 189 107 306
-193 276 269 95 108
-194 110 78 277 289
-195 111 222 290 119
-196 473 112 32 87
-197 212 115 126 185
-198 509 148 118 108
-199 502 217 20 120
-200 121 91 279 273
-201 232 123 136 172
-202 266 280 128 307
-203 146 281 304 109
-204 277 148 282 129
-205 67 137 218 175
-206 396 155 106 131
-207 211 115 270 153
-208 144 266 125 105
-209 177 101 288 104
-210 499 182 239 120
-211 84 207 284 263
-212 110 291 197 285
-213 115 137 467 447
-214 441 125 456 138
-215 56 474 468 19
-216 484 133 57 435
-217 220 199 223 130
-218 287 279 205 108
-219 135 443 127 427
-220 60 337 217 295
-221 308 61 359 283
-222 165 346 195 64
-223 353 68 217 228
-224 290 71 302 360
-225 309 72 249 361
-226 145 310 73 306
-227 311 171 74 362
-228 363 223 312 75
-229 298 313 150 76
-230 77 314 96 174
-231 79 311 280 160
-232 265 80 201 348
-233 299 191 83 315
-234 155 300 170 85
-235 99 286 316 87
-236 94 248 336 317
-237 143 303 107 318
-238 113 94 138 171
-239 210 134 290 61
-240 319 258 139 161
-241 176 320 333 142
-242 143 321 315 173
-243 145 179 322 318
-244 146 180 316 252
-245 147 323 305 186
-246 308 312 149 161
-247 310 159 324 150
-248 236 314 152 163
-249 364 157 278 225
-250 255 365 158 295
-251 189 256 322 159
-252 244 257 160 329
-253 166 324 259 162
-254 148 291 261 164
-255 167 366 325 250
-256 168 367 326 251
-257 169 368 327 252
-258 309 158 369 240
-259 253 170 370 328
-260 147 171 371 329
-261 330 254 355 172
-262 331 169 174 339
-263 211 332 175 340
-264 177 300 334 372
-265 232 178 335 338
-266 267 180 202 208
-267 266 301 181 336
-268 156 182 337 142
-269 356 193 183 338
-270 289 348 207 164
-271 342 191 313 162
-272 304 184 339 373
-273 330 200 185 340
-274 187 341 350 175
-275 374 288 343 192
-276 187 344 345 193
-277 332 345 204 194
-278 353 182 249 141
-279 200 357 347 218
-280 231 375 202 349
-281 354 203 317 186
-282 204 185 350 351
-283 154 188 221 346
-284 211 347 172 351
-285 352 212 358 183
-286 144 354 235 371
-287 352 178 355 218
-288 209 275 321 179
-289 341 356 270 194
-290 224 293 195 239
-291 254 212 335 357
-292 55 58 437 405
-293 363 364 290 139
-294 376 346 425 142
-295 220 386 149 250
-296 165 369 337 426
-297 319 167 377 427
-298 374 168 378 229
-299 233 367 170 379
-300 264 342 234 173
-301 267 380 174 428
-302 176 388 224 381
-303 177 237 370 382
-304 181 203 272 383
-305 245 380 184 327
-306 192 226 372 384
-307 385 202 401 314
-308 221 387 333 246
-309 399 389 225 258
-310 247 390 226 382
-311 231 412 391 227
-312 376 246 381 228
-313 271 392 229 384
-314 248 383 230 307
-315 242 233 378 393
-316 244 235 323 362
-317 375 236 281 394
-318 243 379 237 395
-319 297 429 353 240
-320 363 430 325 241
-321 242 288 326 392
-322 243 393 251 328
-323 407 331 245 316
-324 253 334 247 395
-325 396 320 255 36
-326 397 321 431 256
-327 398 432 257 305
-328 322 400 433 259
-329 401 260 252 373
-330 408 402 261 273
-331 323 434 403 262
-332 277 423 404 263
-333 308 377 435 241
-334 264 324 436 405
-335 265 291 415 406
-336 407 267 236 391
-337 220 268 359 296
-338 265 408 269 404
-339 409 272 262 417
-340 410 273 263 406
-341 289 411 402 274
-342 343 300 390 271
-343 275 342 413 437
-344 276 419 348 414
-345 276 277 415 416
-346 386 222 283 294
-347 279 424 284 416
-348 232 344 270 358
-349 280 371 438 417
-350 418 421 282 274
-351 419 420 282 284
-352 287 420 411 285
-353 319 223 278 360
-354 286 385 412 281
-355 287 421 422 261
-356 289 410 422 269
-357 279 291 423 414
-358 418 424 348 285
-359 429 221 388 337
-360 353 387 224 426
-361 484 386 225 439
-362 227 316 394 428
-363 320 293 228 449
-364 365 249 293 425
-365 364 485 435 250
-366 440 255 387 3
-367 441 299 256 437
-368 442 257 467 383
-369 451 443 258 296
-370 431 444 259 303
-371 286 445 260 349
-372 264 433 446 306
-373 486 447 272 329
-374 275 298 436 448
-375 280 403 447 317
-376 399 312 294 450
-377 297 464 333 131
-378 298 452 446 315
-379 299 453 448 318
-380 454 301 305 471
-381 443 312 302 439
-382 441 310 455 303
-383 368 445 314 304
-384 444 313 456 306
-385 354 432 457 307
-386 346 295 361 449
-387 308 366 487 360
-388 389 488 302 359
-389 396 309 388 15
-390 342 397 310 453
-391 398 311 489 336
-392 321 400 455 313
-393 322 456 315 405
-394 409 317 362 461
-395 452 324 413 318
-396 103 389 325 206
-397 390 18 326 458
-398 391 327 459 54
-399 11 440 309 376
-400 392 42 328 460
-401 454 307 329 461
-402 330 341 462 475
-403 44 331 375 490
-404 463 332 338 483
-405 465 334 292 393
-406 466 335 478 340
-407 323 467 336 438
-408 330 476 468 338
-409 17 469 339 394
-410 474 356 470 340
-411 341 352 466 472
-412 354 442 311 471
-413 473 13 343 395
-414 474 344 357 480
-415 475 345 335 479
-416 476 345 347 472
-417 48 349 459 339
-418 477 358 468 350
-419 344 478 481 351
-420 352 479 470 351
-421 463 355 480 350
-422 355 356 481 482
-423 332 477 357 482
-424 462 347 358 483
-425 451 364 487 294
-426 485 360 296 450
-427 297 507 449 219
-428 486 301 457 362
-429 319 484 430 359
-430 11 429 320 508
-431 13 326 370 491
-432 385 14 469 327
-433 18 492 328 372
-434 331 496 445 118
-435 365 333 216 493
-436 374 334 42 494
-437 495 343 367 292
-438 407 14 509 349
-439 464 117 381 361
-440 57 135 366 399
-441 367 214 382 494
-442 114 368 412 490
-443 369 381 493 219
-444 495 46 370 384
-445 434 489 371 383
-446 4 378 491 372
-447 375 213 503 373
-448 374 112 379 492
-449 363 386 488 427
-450 376 36 510 426
-451 511 369 425 131
-452 46 378 458 395
-453 4 379 390 460
-454 44 401 380 512
-455 112 465 392 382
-456 473 214 393 384
-457 385 48 500 428
-458 397 452 138 43
-459 123 398 153 417
-460 55 453 400 105
-461 496 401 394 54
-462 497 5 402 424
-463 132 421 498 404
-464 377 82 31 439
-465 455 29 9 405
-466 411 499 53 406
-467 407 213 368 500
-468 418 408 215 505
-469 409 432 136 115
-470 420 410 116 504
-471 412 380 118 503
-472 132 411 501 416
-473 456 39 413 196
-474 410 215 501 414
-475 506 45 402 415
-476 408 116 502 416
-477 418 45 423 504
-478 419 498 5 406
-479 420 415 120 505
-480 421 414 502 53
-481 506 1 419 422
-482 497 422 423 120
-483 1 499 424 404
-484 429 510 216 361
-485 365 508 117 426
-486 509 114 373 428
-487 507 387 15 425
-488 3 388 511 449
-489 445 17 391 512
-490 442 47 92 403
-491 431 58 113 446
-492 66 125 433 448
-493 443 27 435 8
-494 34 441 90 436
-495 444 16 437 86
-496 67 126 434 461
-497 462 59 482 98
-498 463 134 478 130
-499 56 210 466 483
-500 33 88 467 457
-501 89 474 2 472
-502 199 476 480 10
-503 51 447 30 471
-504 22 122 477 470
-505 6 468 479 119
-506 111 475 19 481
-507 124 487 41 427
-508 430 485 37 127
-509 198 486 40 438
-510 484 49 21 450
-511 451 12 133 488
-512 454 137 489 52
0

**************