C4graphGraph forms for C4 [ 306, 2 ] = C_306(1,35)

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On this page are computer-accessible forms for the graph C4[ 306, 2 ] = C_306(1,35).

(I) Following is a form readable by MAGMA:

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

(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[ 306, 2 ]
306
-1 2 36 272 306
-2 1 3 37 273
-3 2 4 38 274
-4 275 3 5 39
-5 276 4 6 40
-6 277 5 7 41
-7 278 6 8 42
-8 279 7 9 43
-9 44 280 8 10
-10 11 45 281 9
-11 12 46 282 10
-12 11 13 47 283
-13 12 14 48 284
-14 13 15 49 285
-15 286 14 16 50
-16 287 15 17 51
-17 288 16 18 52
-18 289 17 19 53
-19 290 18 20 54
-20 55 291 19 21
-21 22 56 292 20
-22 23 57 293 21
-23 22 24 58 294
-24 23 25 59 295
-25 24 26 60 296
-26 297 25 27 61
-27 298 26 28 62
-28 299 27 29 63
-29 300 28 30 64
-30 301 29 31 65
-31 66 302 30 32
-32 33 67 303 31
-33 34 68 304 32
-34 33 35 69 305
-35 34 36 70 306
-36 1 35 37 71
-37 2 36 38 72
-38 3 37 39 73
-39 4 38 40 74
-40 5 39 41 75
-41 6 40 42 76
-42 77 7 41 43
-43 44 78 8 42
-44 45 79 9 43
-45 44 46 80 10
-46 11 45 47 81
-47 12 46 48 82
-48 13 47 49 83
-49 14 48 50 84
-50 15 49 51 85
-51 16 50 52 86
-52 17 51 53 87
-53 88 18 52 54
-54 55 89 19 53
-55 56 90 20 54
-56 55 57 91 21
-57 22 56 58 92
-58 23 57 59 93
-59 24 58 60 94
-60 25 59 61 95
-61 26 60 62 96
-62 27 61 63 97
-63 28 62 64 98
-64 99 29 63 65
-65 66 100 30 64
-66 67 101 31 65
-67 66 68 102 32
-68 33 67 69 103
-69 34 68 70 104
-70 35 69 71 105
-71 36 70 72 106
-72 37 71 73 107
-73 38 72 74 108
-74 39 73 75 109
-75 110 40 74 76
-76 77 111 41 75
-77 78 112 42 76
-78 77 79 113 43
-79 44 78 80 114
-80 45 79 81 115
-81 46 80 82 116
-82 47 81 83 117
-83 48 82 84 118
-84 49 83 85 119
-85 50 84 86 120
-86 121 51 85 87
-87 88 122 52 86
-88 89 123 53 87
-89 88 90 124 54
-90 55 89 91 125
-91 56 90 92 126
-92 57 91 93 127
-93 58 92 94 128
-94 59 93 95 129
-95 60 94 96 130
-96 61 95 97 131
-97 132 62 96 98
-98 99 133 63 97
-99 100 134 64 98
-100 99 101 135 65
-101 66 100 102 136
-102 67 101 103 137
-103 68 102 104 138
-104 69 103 105 139
-105 70 104 106 140
-106 71 105 107 141
-107 72 106 108 142
-108 143 73 107 109
-109 110 144 74 108
-110 111 145 75 109
-111 110 112 146 76
-112 77 111 113 147
-113 78 112 114 148
-114 79 113 115 149
-115 80 114 116 150
-116 81 115 117 151
-117 82 116 118 152
-118 83 117 119 153
-119 154 84 118 120
-120 121 155 85 119
-121 122 156 86 120
-122 121 123 157 87
-123 88 122 124 158
-124 89 123 125 159
-125 90 124 126 160
-126 91 125 127 161
-127 92 126 128 162
-128 93 127 129 163
-129 94 128 130 164
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-134 99 133 135 169
-135 100 134 136 170
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-138 103 137 139 173
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-140 105 139 141 175
-141 176 106 140 142
-142 143 177 107 141
-143 144 178 108 142
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-147 112 146 148 182
-148 113 147 149 183
-149 114 148 150 184
-150 115 149 151 185
-151 116 150 152 186
-152 187 117 151 153
-153 154 188 118 152
-154 155 189 119 153
-155 154 156 190 120
-156 121 155 157 191
-157 122 156 158 192
-158 123 157 159 193
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-160 125 159 161 195
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-162 127 161 163 197
-163 198 128 162 164
-164 165 199 129 163
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-170 135 169 171 205
-171 136 170 172 206
-172 137 171 173 207
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-215 180 214 216 250
-216 181 215 217 251
-217 182 216 218 252
-218 253 183 217 219
-219 220 254 184 218
-220 221 255 185 219
-221 220 222 256 186
-222 187 221 223 257
-223 188 222 224 258
-224 189 223 225 259
-225 190 224 226 260
-226 191 225 227 261
-227 192 226 228 262
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-230 231 265 195 229
-231 232 266 196 230
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-248 213 247 249 283
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-258 223 257 259 293
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-261 226 260 262 296
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-267 232 266 268 302
-268 233 267 269 303
-269 234 268 270 304
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-271 236 270 272 306
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-273 2 238 272 274
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-277 242 276 278 6
-278 243 277 279 7
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-290 255 289 291 19
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-292 257 291 293 21
-293 22 258 292 294
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-295 24 260 294 296
-296 297 25 261 295
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-298 297 299 27 263
-299 264 298 300 28
-300 265 299 301 29
-301 266 300 302 30
-302 267 301 303 31
-303 268 302 304 32
-304 33 269 303 305
-305 34 270 304 306
-306 1 35 271 305
0

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