C4graphGraph forms for C4 [ 408, 3 ] = C_408(1,67)

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On this page are computer-accessible forms for the graph C4[ 408, 3 ] = C_408(1,67).

(I) Following is a form readable by MAGMA:

g:=Graph<408|{ {2, 3}, {406, 407}, {404, 405}, {402, 403}, {400, 401}, {398, 399}, {396, 397}, {394, 395}, {392, 393}, {390, 391}, {388, 389}, {386, 387}, {384, 385}, {382, 383}, {380, 381}, {378, 379}, {376, 377}, {374, 375}, {372, 373}, {370, 371}, {368, 369}, {366, 367}, {364, 365}, {362, 363}, {360, 361}, {358, 359}, {356, 357}, {354, 355}, {352, 353}, {350, 351}, {348, 349}, {346, 347}, {344, 345}, {342, 343}, {340, 341}, {338, 339}, {336, 337}, {334, 335}, {332, 333}, {330, 331}, {328, 329}, {326, 327}, {324, 325}, {322, 323}, {320, 321}, {318, 319}, {316, 317}, {314, 315}, {312, 313}, {310, 311}, {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}, {146, 147}, {144, 145}, {142, 143}, {140, 141}, {138, 139}, {136, 137}, {134, 135}, {132, 133}, {130, 131}, {128, 129}, {126, 127}, {124, 125}, {122, 123}, {120, 121}, {118, 119}, {116, 117}, {114, 115}, {112, 113}, {110, 111}, {108, 109}, {106, 107}, {104, 105}, {102, 103}, {100, 101}, {98, 99}, {96, 97}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {86, 87}, {84, 85}, {82, 83}, {80, 81}, {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}, {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}, {1, 2}, {405, 406}, {401, 402}, {397, 398}, {393, 394}, {389, 390}, {385, 386}, {381, 382}, {377, 378}, {373, 374}, {369, 370}, {365, 366}, {361, 362}, {357, 358}, {353, 354}, {349, 350}, {345, 346}, {341, 342}, {337, 338}, {333, 334}, {329, 330}, {325, 326}, {321, 322}, {317, 318}, {313, 314}, {309, 310}, {305, 306}, {301, 302}, {297, 298}, {293, 294}, {289, 290}, {285, 286}, {281, 282}, {277, 278}, {273, 274}, {269, 270}, {145, 146}, {141, 142}, {137, 138}, {133, 134}, {129, 130}, {125, 126}, {121, 122}, {117, 118}, {113, 114}, {109, 110}, {105, 106}, {101, 102}, {97, 98}, {93, 94}, {89, 90}, {85, 86}, {81, 82}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {49, 50}, {53, 54}, {57, 58}, {61, 62}, {65, 66}, {69, 70}, {73, 74}, {77, 78}, {149, 150}, {153, 154}, {157, 158}, {161, 162}, {165, 166}, {169, 170}, {173, 174}, {177, 178}, {181, 182}, {185, 186}, {189, 190}, {193, 194}, {197, 198}, {201, 202}, {205, 206}, {209, 210}, {213, 214}, {217, 218}, {221, 222}, {225, 226}, {229, 230}, {233, 234}, {237, 238}, {241, 242}, {245, 246}, {249, 250}, {253, 254}, {257, 258}, {261, 262}, {265, 266}, {3, 4}, {403, 404}, {395, 396}, {387, 388}, {379, 380}, {371, 372}, {363, 364}, {355, 356}, {347, 348}, {339, 340}, {331, 332}, {323, 324}, {315, 316}, {307, 308}, {299, 300}, {291, 292}, {283, 284}, {275, 276}, {139, 140}, {131, 132}, {123, 124}, {115, 116}, {107, 108}, {99, 100}, {91, 92}, {83, 84}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {51, 52}, {59, 60}, {67, 68}, {75, 76}, {147, 148}, {155, 156}, {163, 164}, {171, 172}, {179, 180}, {187, 188}, {195, 196}, {203, 204}, {211, 212}, {219, 220}, {227, 228}, {235, 236}, {243, 244}, {251, 252}, {259, 260}, {267, 268}, {7, 8}, {407, 408}, {391, 392}, {375, 376}, {359, 360}, {343, 344}, {327, 328}, {311, 312}, {295, 296}, {279, 280}, {135, 136}, {119, 120}, {103, 104}, {87, 88}, {23, 24}, {39, 40}, {55, 56}, {71, 72}, {151, 152}, {167, 168}, {183, 184}, {199, 200}, {215, 216}, {231, 232}, {247, 248}, {263, 264}, {15, 16}, {399, 400}, {367, 368}, {335, 336}, {303, 304}, {271, 272}, {143, 144}, {111, 112}, {79, 80}, {47, 48}, {175, 176}, {207, 208}, {239, 240}, {31, 32}, {351, 352}, {287, 288}, {95, 96}, {159, 160}, {223, 224}, {4, 71}, {316, 383}, {312, 379}, {308, 375}, {304, 371}, {300, 367}, {296, 363}, {292, 359}, {288, 355}, {284, 351}, {280, 347}, {276, 343}, {272, 339}, {268, 335}, {144, 211}, {140, 207}, {136, 203}, {132, 199}, {128, 195}, {8, 75}, {12, 79}, {16, 83}, {20, 87}, {24, 91}, {28, 95}, {32, 99}, {36, 103}, {40, 107}, {44, 111}, {48, 115}, {52, 119}, {56, 123}, {60, 127}, {148, 215}, {152, 219}, {156, 223}, {160, 227}, {164, 231}, {168, 235}, {172, 239}, {176, 243}, {180, 247}, {184, 251}, {188, 255}, {256, 323}, {260, 327}, {264, 331}, {1, 68}, {315, 382}, {313, 380}, {307, 374}, {305, 372}, {299, 366}, {297, 364}, {291, 358}, {289, 356}, {283, 350}, {281, 348}, {275, 342}, {273, 340}, {145, 212}, {139, 206}, {137, 204}, {131, 198}, {129, 196}, {3, 70}, {9, 76}, {11, 78}, {17, 84}, {19, 86}, {25, 92}, {27, 94}, {33, 100}, {35, 102}, {41, 108}, {43, 110}, {49, 116}, {51, 118}, {57, 124}, {59, 126}, {147, 214}, {153, 220}, {155, 222}, {161, 228}, {163, 230}, {169, 236}, {171, 238}, {177, 244}, {179, 246}, {185, 252}, {187, 254}, {257, 324}, {259, 326}, {265, 332}, {267, 334}, {2, 69}, {314, 381}, {306, 373}, {298, 365}, {290, 357}, {282, 349}, {274, 341}, {138, 205}, {130, 197}, {10, 77}, {18, 85}, {26, 93}, {34, 101}, {42, 109}, {50, 117}, {58, 125}, {146, 213}, {154, 221}, {162, 229}, {170, 237}, {178, 245}, {186, 253}, {258, 325}, {266, 333}, {5, 72}, {311, 378}, {309, 376}, {295, 362}, {293, 360}, {279, 346}, {277, 344}, {135, 202}, {133, 200}, {7, 74}, {21, 88}, {23, 90}, {37, 104}, {39, 106}, {53, 120}, {55, 122}, {149, 216}, {151, 218}, {165, 232}, {167, 234}, {181, 248}, {183, 250}, {261, 328}, {263, 330}, {6, 73}, {310, 377}, {294, 361}, {278, 345}, {134, 201}, {22, 89}, {38, 105}, {54, 121}, {150, 217}, {166, 233}, {182, 249}, {262, 329}, {13, 80}, {303, 370}, {301, 368}, {271, 338}, {269, 336}, {143, 210}, {141, 208}, {15, 82}, {45, 112}, {47, 114}, {173, 240}, {175, 242}, {14, 81}, {302, 369}, {270, 337}, {142, 209}, {46, 113}, {174, 241}, {29, 96}, {287, 354}, {285, 352}, {31, 98}, {157, 224}, {159, 226}, {30, 97}, {319, 320}, {286, 353}, {63, 64}, {158, 225}, {191, 192}, {61, 128}, {319, 386}, {317, 384}, {127, 194}, {125, 192}, {63, 130}, {62, 129}, {318, 385}, {126, 193}, {64, 131}, {340, 407}, {336, 403}, {332, 399}, {328, 395}, {324, 391}, {320, 387}, {124, 191}, {120, 187}, {116, 183}, {112, 179}, {108, 175}, {104, 171}, {100, 167}, {96, 163}, {92, 159}, {88, 155}, {84, 151}, {80, 147}, {68, 135}, {72, 139}, {76, 143}, {65, 132}, {339, 406}, {337, 404}, {331, 398}, {329, 396}, {323, 390}, {321, 388}, {123, 190}, {121, 188}, {115, 182}, {113, 180}, {107, 174}, {105, 172}, {99, 166}, {97, 164}, {91, 158}, {89, 156}, {83, 150}, {81, 148}, {67, 134}, {73, 140}, {75, 142}, {66, 133}, {338, 405}, {330, 397}, {322, 389}, {122, 189}, {114, 181}, {106, 173}, {98, 165}, {90, 157}, {82, 149}, {74, 141}, {69, 136}, {341, 408}, {327, 394}, {325, 392}, {119, 186}, {117, 184}, {103, 170}, {101, 168}, {87, 154}, {85, 152}, {71, 138}, {70, 137}, {326, 393}, {118, 185}, {102, 169}, {86, 153}, {77, 144}, {335, 402}, {333, 400}, {111, 178}, {109, 176}, {79, 146}, {78, 145}, {334, 401}, {110, 177}, {93, 160}, {95, 162}, {94, 161}, {383, 384}, {127, 128}, {2, 343}, {8, 349}, {10, 351}, {32, 373}, {34, 375}, {40, 381}, {42, 383}, {1, 342}, {9, 350}, {33, 374}, {41, 382}, {3, 344}, {7, 348}, {35, 376}, {39, 380}, {4, 345}, {6, 347}, {36, 377}, {38, 379}, {5, 346}, {37, 378}, {11, 352}, {15, 356}, {27, 368}, {31, 372}, {12, 353}, {14, 355}, {28, 369}, {30, 371}, {13, 354}, {29, 370}, {16, 357}, {18, 359}, {24, 365}, {26, 367}, {17, 358}, {25, 366}, {19, 360}, {23, 364}, {20, 361}, {22, 363}, {21, 362}, {1, 408}, {43, 384}, {47, 388}, {59, 400}, {63, 404}, {44, 385}, {46, 387}, {60, 401}, {62, 403}, {45, 386}, {61, 402}, {48, 389}, {50, 391}, {56, 397}, {58, 399}, {49, 390}, {57, 398}, {51, 392}, {55, 396}, {52, 393}, {54, 395}, {189, 256}, {191, 258}, {253, 320}, {255, 322}, {53, 394}, {190, 257}, {254, 321}, {192, 259}, {196, 263}, {200, 267}, {204, 271}, {208, 275}, {212, 279}, {216, 283}, {220, 287}, {224, 291}, {228, 295}, {232, 299}, {236, 303}, {240, 307}, {244, 311}, {248, 315}, {252, 319}, {193, 260}, {195, 262}, {201, 268}, {203, 270}, {209, 276}, {211, 278}, {217, 284}, {219, 286}, {225, 292}, {227, 294}, {233, 300}, {235, 302}, {241, 308}, {243, 310}, {249, 316}, {251, 318}, {194, 261}, {202, 269}, {210, 277}, {218, 285}, {226, 293}, {234, 301}, {242, 309}, {250, 317}, {197, 264}, {199, 266}, {213, 280}, {215, 282}, {229, 296}, {231, 298}, {245, 312}, {247, 314}, {198, 265}, {214, 281}, {230, 297}, {246, 313}, {64, 405}, {66, 407}, {65, 406}, {67, 408}, {205, 272}, {207, 274}, {237, 304}, {239, 306}, {206, 273}, {238, 305}, {221, 288}, {223, 290}, {222, 289}, {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, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408)
b: (2, 342)(3, 275)(4, 208)(5, 141)(6, 74)(8, 348)(9, 281)(10, 214)(11, 147)(12, 80)(14, 354)(15, 287)(16, 220)(17, 153)(18, 86)(20, 360)(21, 293)(22, 226)(23, 159)(24, 92)(26, 366)(27, 299)(28, 232)(29, 165)(30, 98)(32, 372)(33, 305)(34, 238)(35, 171)(36, 104)(38, 378)(39, 311)(40, 244)(41, 177)(42, 110)(44, 384)(45, 317)(46, 250)(47, 183)(48, 116)(50, 390)(51, 323)(52, 256)(53, 189)(54, 122)(56, 396)(57, 329)(58, 262)(59, 195)(60, 128)(62, 402)(63, 335)(64, 268)(65, 201)(66, 134)(68, 408)(69, 341)(70, 274)(71, 207)(72, 140)(75, 347)(76, 280)(77, 213)(78, 146)(81, 353)(82, 286)(83, 219)(84, 152)(87, 359)(88, 292)(89, 225)(90, 158)(93, 365)(94, 298)(95, 231)(96, 164)(99, 371)(100, 304)(101, 237)(102, 170)(105, 377)(106, 310)(107, 243)(108, 176)(111, 383)(112, 316)(113, 249)(114, 182)(117, 389)(118, 322)(119, 255)(120, 188)(123, 395)(124, 328)(125, 261)(126, 194)(129, 401)(130, 334)(131, 267)(132, 200)(135, 407)(136, 340)(137, 273)(138, 206)(142, 346)(143, 279)(144, 212)(148, 352)(149, 285)(150, 218)(154, 358)(155, 291)(156, 224)(160, 364)(161, 297)(162, 230)(166, 370)(167, 303)(168, 236)(172, 376)(173, 309)(174, 242)(178, 382)(179, 315)(180, 248)(184, 388)(185, 321)(186, 254)(190, 394)(191, 327)(192, 260)(196, 400)(197, 333)(198, 266)(202, 406)(203, 339)(204, 272)(209, 345)(210, 278)(215, 351)(216, 284)(221, 357)(222, 290)(227, 363)(228, 296)(233, 369)(234, 302)(239, 375)(240, 308)(245, 381)(246, 314)(251, 387)(252, 320)(257, 393)(258, 326)(263, 399)(264, 332)(269, 405)(270, 338)(276, 344)(282, 350)(288, 356)(294, 362)(300, 368)(306, 374)(312, 380)(318, 386)(324, 392)(330, 398)(336, 404)
c: (2, 68)(3, 135)(4, 202)(5, 269)(6, 336)(7, 403)(8, 62)(9, 129)(10, 196)(11, 263)(12, 330)(13, 397)(14, 56)(15, 123)(16, 190)(17, 257)(18, 324)(19, 391)(20, 50)(21, 117)(22, 184)(23, 251)(24, 318)(25, 385)(26, 44)(27, 111)(28, 178)(29, 245)(30, 312)(31, 379)(32, 38)(33, 105)(34, 172)(35, 239)(36, 306)(37, 373)(39, 99)(40, 166)(41, 233)(42, 300)(43, 367)(45, 93)(46, 160)(47, 227)(48, 294)(49, 361)(51, 87)(52, 154)(53, 221)(54, 288)(55, 355)(57, 81)(58, 148)(59, 215)(60, 282)(61, 349)(63, 75)(64, 142)(65, 209)(66, 276)(67, 343)(70, 136)(71, 203)(72, 270)(73, 337)(74, 404)(76, 130)(77, 197)(78, 264)(79, 331)(80, 398)(82, 124)(83, 191)(84, 258)(85, 325)(86, 392)(88, 118)(89, 185)(90, 252)(91, 319)(92, 386)(94, 112)(95, 179)(96, 246)(97, 313)(98, 380)(100, 106)(101, 173)(102, 240)(103, 307)(104, 374)(107, 167)(108, 234)(109, 301)(110, 368)(113, 161)(114, 228)(115, 295)(116, 362)(119, 155)(120, 222)(121, 289)(122, 356)(125, 149)(126, 216)(127, 283)(128, 350)(131, 143)(132, 210)(133, 277)(134, 344)(138, 204)(139, 271)(140, 338)(141, 405)(144, 198)(145, 265)(146, 332)(147, 399)(150, 192)(151, 259)(152, 326)(153, 393)(156, 186)(157, 253)(158, 320)(159, 387)(162, 180)(163, 247)(164, 314)(165, 381)(168, 174)(169, 241)(170, 308)(171, 375)(175, 235)(176, 302)(177, 369)(181, 229)(182, 296)(183, 363)(187, 223)(188, 290)(189, 357)(193, 217)(194, 284)(195, 351)(199, 211)(200, 278)(201, 345)(206, 272)(207, 339)(208, 406)(212, 266)(213, 333)(214, 400)(218, 260)(219, 327)(220, 394)(224, 254)(225, 321)(226, 388)(230, 248)(231, 315)(232, 382)(236, 242)(237, 309)(238, 376)(243, 303)(244, 370)(249, 297)(250, 364)(255, 291)(256, 358)(261, 285)(262, 352)(267, 279)(268, 346)(274, 340)(275, 407)(280, 334)(281, 401)(286, 328)(287, 395)(292, 322)(293, 389)(298, 316)(299, 383)(304, 310)(305, 377)(311, 371)(317, 365)(323, 359)(329, 353)(335, 347)(342, 408)(348, 402)(354, 396)(360, 390)(366, 384)(372, 378)

(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[ 408, 3 ]
408
-1 342 408 2 68
-2 1 343 3 69
-3 2 344 4 70
-4 3 345 5 71
-5 4 346 6 72
-6 5 347 7 73
-7 6 348 8 74
-8 7 349 9 75
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-10 11 77 9 351
-11 352 12 78 10
-12 11 353 13 79
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-23 22 364 24 90
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-177 110 176 178 244
-178 111 177 179 245
-179 112 178 180 246
-180 113 179 181 247
-181 114 180 182 248
-182 115 181 183 249
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-184 117 183 185 251
-185 118 184 186 252
-186 187 253 119 185
-187 188 254 120 186
-188 121 187 189 255
-189 122 188 190 256
-190 123 189 191 257
-191 124 190 192 258
-192 125 191 193 259
-193 126 192 194 260
-194 127 193 195 261
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0

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