C4graphGraph forms for C4 [ 312, 3 ] = C_312(1,53)

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On this page are computer-accessible forms for the graph C4[ 312, 3 ] = C_312(1,53).

(I) Following is a form readable by MAGMA:

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

(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[ 312, 3 ]
312
-1 2 312 260 54
-2 55 1 3 261
-3 56 2 4 262
-4 57 3 5 263
-5 264 58 4 6
-6 265 59 5 7
-7 266 60 6 8
-8 267 61 7 9
-9 268 62 8 10
-10 11 269 63 9
-11 12 270 64 10
-12 11 13 271 65
-13 66 12 14 272
-14 67 13 15 273
-15 68 14 16 274
-16 275 69 15 17
-17 276 70 16 18
-18 277 71 17 19
-19 278 72 18 20
-20 279 73 19 21
-21 22 280 74 20
-22 23 281 75 21
-23 22 24 282 76
-24 77 23 25 283
-25 78 24 26 284
-26 79 25 27 285
-27 286 80 26 28
-28 287 81 27 29
-29 288 82 28 30
-30 289 83 29 31
-31 290 84 30 32
-32 33 291 85 31
-33 34 292 86 32
-34 33 35 293 87
-35 88 34 36 294
-36 89 35 37 295
-37 90 36 38 296
-38 297 91 37 39
-39 298 92 38 40
-40 299 93 39 41
-41 300 94 40 42
-42 301 95 41 43
-43 44 302 96 42
-44 45 303 97 43
-45 44 46 304 98
-46 99 45 47 305
-47 100 46 48 306
-48 101 47 49 307
-49 308 102 48 50
-50 309 103 49 51
-51 310 104 50 52
-52 311 105 51 53
-53 312 106 52 54
-54 55 1 107 53
-55 56 2 108 54
-56 55 57 3 109
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-58 111 57 59 5
-59 112 58 60 6
-60 113 59 61 7
-61 114 60 62 8
-62 115 61 63 9
-63 116 62 64 10
-64 11 117 63 65
-65 66 12 118 64
-66 67 13 119 65
-67 66 68 14 120
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-69 122 68 70 16
-70 123 69 71 17
-71 124 70 72 18
-72 125 71 73 19
-73 126 72 74 20
-74 127 73 75 21
-75 22 128 74 76
-76 77 23 129 75
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-80 133 79 81 27
-81 134 80 82 28
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-84 137 83 85 31
-85 138 84 86 32
-86 33 139 85 87
-87 88 34 140 86
-88 89 35 141 87
-89 88 90 36 142
-90 143 89 91 37
-91 144 90 92 38
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-93 146 92 94 40
-94 147 93 95 41
-95 148 94 96 42
-96 149 95 97 43
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-100 99 101 47 153
-101 154 100 102 48
-102 155 101 103 49
-103 156 102 104 50
-104 157 103 105 51
-105 158 104 106 52
-106 159 105 107 53
-107 160 106 108 54
-108 55 161 107 109
-109 110 56 162 108
-110 111 57 163 109
-111 110 112 58 164
-112 165 111 113 59
-113 166 112 114 60
-114 167 113 115 61
-115 168 114 116 62
-116 169 115 117 63
-117 170 116 118 64
-118 171 117 119 65
-119 66 172 118 120
-120 121 67 173 119
-121 122 68 174 120
-122 121 123 69 175
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-141 88 194 140 142
-142 143 89 195 141
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-219 220 166 272 218
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-221 220 222 168 274
-222 275 221 223 169
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-294 35 293 295 241
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-302 301 303 249 43
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-304 45 303 305 251
-305 46 304 306 252
-306 253 47 305 307
-307 308 254 48 306
-308 309 255 49 307
-309 308 310 256 50
-310 309 311 257 51
-311 310 312 258 52
-312 1 311 259 53
0

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