C4graphGraph forms for C4 [ 315, 1 ] = C_315(1,64)

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On this page are computer-accessible forms for the graph C4[ 315, 1 ] = C_315(1,64).

(I) Following is a form readable by MAGMA:

g:=Graph<315|{ {2, 3}, {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}, {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}, {94, 95}, {92, 93}, {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}, {52, 53}, {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}, {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}, {1, 2}, {313, 314}, {309, 310}, {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}, {93, 94}, {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}, {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}, {177, 178}, {181, 182}, {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}, {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}, {179, 180}, {7, 8}, {311, 312}, {295, 296}, {279, 280}, {263, 264}, {247, 248}, {231, 232}, {215, 216}, {199, 200}, {87, 88}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {103, 104}, {119, 120}, {135, 136}, {151, 152}, {167, 168}, {183, 184}, {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, 65}, {191, 255}, {190, 254}, {189, 253}, {188, 252}, {187, 251}, {186, 250}, {185, 249}, {184, 248}, {63, 127}, {62, 126}, {61, 125}, {60, 124}, {59, 123}, {58, 122}, {57, 121}, {56, 120}, {55, 119}, {54, 118}, {53, 117}, {52, 116}, {51, 115}, {2, 66}, {3, 67}, {4, 68}, {5, 69}, {6, 70}, {7, 71}, {8, 72}, {9, 73}, {10, 74}, {11, 75}, {12, 76}, {13, 77}, {14, 78}, {15, 79}, {16, 80}, {17, 81}, {18, 82}, {19, 83}, {20, 84}, {21, 85}, {22, 86}, {23, 87}, {24, 88}, {25, 89}, {26, 90}, {27, 91}, {28, 92}, {29, 93}, {30, 94}, {31, 95}, {32, 96}, {33, 97}, {34, 98}, {35, 99}, {36, 100}, {37, 101}, {38, 102}, {39, 103}, {40, 104}, {41, 105}, {42, 106}, {43, 107}, {44, 108}, {45, 109}, {46, 110}, {47, 111}, {48, 112}, {49, 113}, {50, 114}, {128, 192}, {129, 193}, {130, 194}, {131, 195}, {132, 196}, {133, 197}, {134, 198}, {135, 199}, {136, 200}, {137, 201}, {138, 202}, {139, 203}, {140, 204}, {141, 205}, {142, 206}, {143, 207}, {144, 208}, {145, 209}, {146, 210}, {147, 211}, {148, 212}, {149, 213}, {150, 214}, {151, 215}, {152, 216}, {153, 217}, {154, 218}, {155, 219}, {156, 220}, {157, 221}, {158, 222}, {159, 223}, {160, 224}, {161, 225}, {162, 226}, {163, 227}, {164, 228}, {165, 229}, {166, 230}, {167, 231}, {168, 232}, {169, 233}, {170, 234}, {171, 235}, {172, 236}, {173, 237}, {174, 238}, {175, 239}, {176, 240}, {177, 241}, {178, 242}, {179, 243}, {180, 244}, {181, 245}, {182, 246}, {183, 247}, {63, 64}, {191, 192}, {64, 128}, {95, 159}, {94, 158}, {93, 157}, {92, 156}, {91, 155}, {90, 154}, {89, 153}, {88, 152}, {87, 151}, {86, 150}, {85, 149}, {84, 148}, {83, 147}, {82, 146}, {81, 145}, {80, 144}, {79, 143}, {78, 142}, {77, 141}, {76, 140}, {75, 139}, {74, 138}, {73, 137}, {72, 136}, {71, 135}, {70, 134}, {69, 133}, {68, 132}, {67, 131}, {66, 130}, {65, 129}, {96, 160}, {97, 161}, {98, 162}, {99, 163}, {100, 164}, {101, 165}, {102, 166}, {103, 167}, {104, 168}, {105, 169}, {106, 170}, {107, 171}, {108, 172}, {109, 173}, {110, 174}, {111, 175}, {112, 176}, {113, 177}, {114, 178}, {115, 179}, {116, 180}, {117, 181}, {118, 182}, {119, 183}, {120, 184}, {121, 185}, {122, 186}, {123, 187}, {124, 188}, {125, 189}, {126, 190}, {127, 191}, {4, 255}, {1, 252}, {3, 254}, {2, 253}, {127, 128}, {5, 256}, {63, 314}, {61, 312}, {55, 306}, {53, 304}, {7, 258}, {13, 264}, {15, 266}, {21, 272}, {23, 274}, {29, 280}, {31, 282}, {37, 288}, {39, 290}, {45, 296}, {47, 298}, {6, 257}, {62, 313}, {54, 305}, {14, 265}, {22, 273}, {30, 281}, {38, 289}, {46, 297}, {8, 259}, {60, 311}, {56, 307}, {12, 263}, {24, 275}, {28, 279}, {40, 291}, {44, 295}, {9, 260}, {59, 310}, {57, 308}, {11, 262}, {25, 276}, {27, 278}, {41, 292}, {43, 294}, {10, 261}, {58, 309}, {26, 277}, {42, 293}, {16, 267}, {52, 303}, {20, 271}, {48, 299}, {17, 268}, {51, 302}, {19, 270}, {49, 300}, {18, 269}, {50, 301}, {1, 315}, {32, 283}, {36, 287}, {33, 284}, {35, 286}, {34, 285}, {64, 315}, {192, 256}, {251, 315}, {250, 314}, {249, 313}, {248, 312}, {247, 311}, {246, 310}, {245, 309}, {244, 308}, {243, 307}, {242, 306}, {241, 305}, {240, 304}, {239, 303}, {238, 302}, {237, 301}, {236, 300}, {235, 299}, {234, 298}, {233, 297}, {232, 296}, {231, 295}, {230, 294}, {229, 293}, {228, 292}, {227, 291}, {226, 290}, {225, 289}, {224, 288}, {223, 287}, {222, 286}, {221, 285}, {220, 284}, {219, 283}, {218, 282}, {217, 281}, {216, 280}, {215, 279}, {214, 278}, {213, 277}, {212, 276}, {211, 275}, {210, 274}, {209, 273}, {208, 272}, {207, 271}, {206, 270}, {205, 269}, {204, 268}, {203, 267}, {202, 266}, {201, 265}, {200, 264}, {199, 263}, {198, 262}, {197, 261}, {196, 260}, {195, 259}, {194, 258}, {193, 257}, {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: (2, 65)(3, 129)(4, 193)(5, 257)(7, 70)(8, 134)(9, 198)(10, 262)(12, 75)(13, 139)(14, 203)(15, 267)(17, 80)(18, 144)(19, 208)(20, 272)(22, 85)(23, 149)(24, 213)(25, 277)(27, 90)(28, 154)(29, 218)(30, 282)(32, 95)(33, 159)(34, 223)(35, 287)(37, 100)(38, 164)(39, 228)(40, 292)(42, 105)(43, 169)(44, 233)(45, 297)(47, 110)(48, 174)(49, 238)(50, 302)(52, 115)(53, 179)(54, 243)(55, 307)(57, 120)(58, 184)(59, 248)(60, 312)(62, 125)(63, 189)(64, 253)(67, 130)(68, 194)(69, 258)(72, 135)(73, 199)(74, 263)(77, 140)(78, 204)(79, 268)(82, 145)(83, 209)(84, 273)(87, 150)(88, 214)(89, 278)(92, 155)(93, 219)(94, 283)(97, 160)(98, 224)(99, 288)(102, 165)(103, 229)(104, 293)(107, 170)(108, 234)(109, 298)(112, 175)(113, 239)(114, 303)(117, 180)(118, 244)(119, 308)(122, 185)(123, 249)(124, 313)(127, 190)(128, 254)(132, 195)(133, 259)(137, 200)(138, 264)(142, 205)(143, 269)(147, 210)(148, 274)(152, 215)(153, 279)(157, 220)(158, 284)(162, 225)(163, 289)(167, 230)(168, 294)(172, 235)(173, 299)(177, 240)(178, 304)(182, 245)(183, 309)(187, 250)(188, 314)(192, 255)(197, 260)(202, 265)(207, 270)(212, 275)(217, 280)(222, 285)(227, 290)(232, 295)(237, 300)(242, 305)(247, 310)(252, 315)
b: (2, 252)(3, 188)(4, 124)(5, 60)(6, 311)(7, 247)(8, 183)(9, 119)(10, 55)(11, 306)(12, 242)(13, 178)(14, 114)(15, 50)(16, 301)(17, 237)(18, 173)(19, 109)(20, 45)(21, 296)(22, 232)(23, 168)(24, 104)(25, 40)(26, 291)(27, 227)(28, 163)(29, 99)(30, 35)(31, 286)(32, 222)(33, 158)(34, 94)(36, 281)(37, 217)(38, 153)(39, 89)(41, 276)(42, 212)(43, 148)(44, 84)(46, 271)(47, 207)(48, 143)(49, 79)(51, 266)(52, 202)(53, 138)(54, 74)(56, 261)(57, 197)(58, 133)(59, 69)(61, 256)(62, 192)(63, 128)(65, 315)(66, 251)(67, 187)(68, 123)(70, 310)(71, 246)(72, 182)(73, 118)(75, 305)(76, 241)(77, 177)(78, 113)(80, 300)(81, 236)(82, 172)(83, 108)(85, 295)(86, 231)(87, 167)(88, 103)(90, 290)(91, 226)(92, 162)(93, 98)(95, 285)(96, 221)(97, 157)(100, 280)(101, 216)(102, 152)(105, 275)(106, 211)(107, 147)(110, 270)(111, 206)(112, 142)(115, 265)(116, 201)(117, 137)(120, 260)(121, 196)(122, 132)(125, 255)(126, 191)(129, 314)(130, 250)(131, 186)(134, 309)(135, 245)(136, 181)(139, 304)(140, 240)(141, 176)(144, 299)(145, 235)(146, 171)(149, 294)(150, 230)(151, 166)(154, 289)(155, 225)(156, 161)(159, 284)(160, 220)(164, 279)(165, 215)(169, 274)(170, 210)(174, 269)(175, 205)(179, 264)(180, 200)(184, 259)(185, 195)(189, 254)(193, 313)(194, 249)(198, 308)(199, 244)(203, 303)(204, 239)(208, 298)(209, 234)(213, 293)(214, 229)(218, 288)(219, 224)(223, 283)(228, 278)(233, 273)(238, 268)(243, 263)(248, 258)(257, 312)(262, 307)(267, 302)(272, 297)(277, 292)(282, 287)
c: (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)

(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[ 315, 1 ]
315
-1 2 315 65 252
-2 66 253 1 3
-3 67 254 2 4
-4 68 255 3 5
-5 69 256 4 6
-6 70 257 5 7
-7 71 258 6 8
-8 72 259 7 9
-9 73 260 8 10
-10 11 74 261 9
-11 12 75 262 10
-12 11 13 76 263
-13 77 264 12 14
-14 78 265 13 15
-15 79 266 14 16
-16 80 267 15 17
-17 81 268 16 18
-18 82 269 17 19
-19 83 270 18 20
-20 84 271 19 21
-21 22 85 272 20
-22 23 86 273 21
-23 22 24 87 274
-24 88 275 23 25
-25 89 276 24 26
-26 90 277 25 27
-27 91 278 26 28
-28 92 279 27 29
-29 93 280 28 30
-30 94 281 29 31
-31 95 282 30 32
-32 33 96 283 31
-33 34 97 284 32
-34 33 35 98 285
-35 99 286 34 36
-36 100 287 35 37
-37 101 288 36 38
-38 102 289 37 39
-39 103 290 38 40
-40 104 291 39 41
-41 105 292 40 42
-42 106 293 41 43
-43 44 107 294 42
-44 45 108 295 43
-45 44 46 109 296
-46 110 297 45 47
-47 111 298 46 48
-48 112 299 47 49
-49 113 300 48 50
-50 114 301 49 51
-51 115 302 50 52
-52 116 303 51 53
-53 117 304 52 54
-54 55 118 305 53
-55 56 119 306 54
-56 55 57 120 307
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-66 67 2 130 65
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-69 133 68 70 5
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-76 77 12 140 75
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-96 160 95 97 32
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-113 177 112 114 49
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-118 182 117 119 54
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-121 122 57 185 120
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-128 192 127 129 64
-129 193 128 130 65
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-309 308 310 58 245
-310 309 311 59 246
-311 310 312 60 247
-312 311 313 61 248
-313 312 314 62 249
-314 313 315 63 250
-315 1 314 64 251
0

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