C4graphGraph forms for C4 [ 512, 185 ] = UG(ATD[512,395])

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On this page are computer-accessible forms for the graph C4[ 512, 185 ] = UG(ATD[512,395]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {60, 61} under the group generated by the following permutations:

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

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

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