C4graphGraph forms for C4 [ 300, 17 ] = MSZ(60,5,11,2)

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On this page are computer-accessible forms for the graph C4[ 300, 17 ] = MSZ(60,5,11,2).

(I) Following is a form readable by MAGMA:

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

(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[ 300, 17 ]
300
-1 110 132 2 60
-2 253 1 3 171
-3 2 4 292 194
-4 233 3 5 75
-5 4 114 136 6
-6 257 5 7 175
-7 198 6 8 296
-8 79 237 7 9
-9 8 118 140 10
-10 11 179 261 9
-11 12 300 202 10
-12 11 13 181 83
-13 12 144 14 62
-14 265 13 123 15
-15 244 14 16 206
-16 15 17 185 87
-17 66 16 148 18
-18 269 17 127 19
-19 210 248 18 20
-20 189 91 19 21
-21 22 70 20 152
-22 23 273 21 131
-23 22 24 214 252
-24 23 25 193 95
-25 24 156 26 74
-26 277 25 135 27
-27 256 26 28 218
-28 99 27 29 197
-29 78 28 160 30
-30 281 29 139 31
-31 222 260 30 32
-32 33 201 103 31
-33 34 82 32 164
-34 33 143 35 285
-35 264 34 36 226
-36 35 37 205 107
-37 36 168 38 86
-38 289 37 147 39
-39 268 38 40 230
-40 209 111 39 41
-41 90 40 172 42
-42 293 41 151 43
-43 44 234 272 42
-44 45 213 115 43
-45 44 176 46 94
-46 297 45 155 47
-47 276 46 48 238
-48 47 49 217 119
-49 48 180 50 98
-50 49 159 51 241
-51 280 50 182 52
-52 221 51 63 53
-53 102 124 52 54
-54 55 245 53 163
-55 56 284 54 186
-56 55 67 57 225
-57 56 58 106 128
-58 57 167 59 249
-59 288 58 190 60
-60 1 59 71 229
-61 170 192 62 120
-62 231 13 61 63
-63 254 62 52 64
-64 135 293 63 65
-65 66 64 174 196
-66 67 235 17 65
-67 66 56 68 258
-68 297 67 69 139
-69 68 178 200 70
-70 69 71 239 21
-71 70 60 72 262
-72 143 71 73 241
-73 122 72 204 74
-74 25 73 183 75
-75 266 4 74 76
-76 77 245 147 75
-77 78 126 76 208
-78 77 187 79 29
-79 78 80 270 8
-80 79 81 249 151
-81 80 212 82 130
-82 33 81 191 83
-83 12 82 84 274
-84 253 155 83 85
-85 134 84 216 86
-86 37 85 195 87
-87 88 278 16 86
-88 89 257 159 87
-89 88 220 90 138
-90 89 199 91 41
-91 90 92 282 20
-92 91 93 261 163
-93 92 224 94 142
-94 45 93 203 95
-95 286 24 94 96
-96 265 167 95 97
-97 146 96 228 98
-98 99 49 97 207
-99 100 290 28 98
-100 99 101 269 171
-101 100 232 102 150
-102 101 211 103 53
-103 102 104 294 32
-104 103 105 273 175
-105 154 104 236 106
-106 57 105 215 107
-107 298 36 106 108
-108 277 179 107 109
-109 110 158 108 240
-110 1 111 109 219
-111 110 242 112 40
-112 111 123 113 281
-113 112 114 162 184
-114 113 223 5 115
-115 44 114 246 116
-116 115 127 117 285
-117 166 188 116 118
-118 117 227 9 119
-119 48 118 250 120
-120 289 61 119 131
-121 122 180 230 252
-122 121 123 291 73
-123 122 112 14 124
-124 123 125 195 53
-125 124 234 256 126
-126 77 125 127 295
-127 126 116 18 128
-128 199 57 127 129
-129 128 238 260 130
-130 299 81 129 131
-131 22 132 130 120
-132 1 133 203 131
-133 132 264 134 182
-134 133 243 135 85
-135 134 26 136 64
-136 135 5 137 207
-137 136 268 138 186
-138 89 137 247 139
-139 68 138 30 140
-140 211 139 9 141
-141 190 140 272 142
-142 143 93 141 251
-143 34 144 72 142
-144 143 13 145 215
-145 144 276 146 194
-146 145 255 147 97
-147 146 38 148 76
-148 147 17 149 219
-149 198 148 280 150
-150 101 149 259 151
-151 80 150 42 152
-152 223 151 21 153
-153 154 202 152 284
-154 155 105 153 263
-155 154 46 156 84
-156 155 25 157 227
-157 156 288 158 206
-158 157 267 159 109
-159 88 158 50 160
-160 231 159 29 161
-161 210 160 292 162
-162 113 161 271 163
-163 92 162 54 164
-164 33 165 235 163
-165 166 214 164 296
-166 165 275 167 117
-167 166 58 168 96
-168 167 37 169 239
-169 168 300 170 218
-170 169 279 61 171
-171 100 2 170 172
-172 171 183 41 173
-173 222 244 172 174
-174 173 283 65 175
-175 176 104 6 174
-176 187 45 177 175
-177 176 178 226 248
-178 177 287 69 179
-179 178 180 108 10
-180 121 179 191 49
-181 12 290 182 240
-182 133 181 51 183
-183 182 172 74 184
-184 255 113 183 185
-185 16 184 294 186
-186 55 187 137 185
-187 176 78 188 186
-188 187 189 259 117
-189 188 298 190 20
-190 189 59 191 141
-191 190 180 82 192
-192 191 61 193 263
-193 242 24 192 194
-194 145 3 193 195
-195 124 194 86 196
-196 267 195 65 197
-197 198 246 28 196
-198 199 149 7 197
-199 198 90 200 128
-200 199 69 201 271
-201 200 202 250 32
-202 11 201 203 153
-203 132 202 94 204
-204 275 203 73 205
-205 254 36 204 206
-206 157 15 205 207
-207 136 206 98 208
-208 77 209 279 207
-209 210 258 40 208
-210 209 211 161 19
-211 210 102 212 140
-212 211 81 213 283
-213 44 212 214 262
-214 165 23 213 215
-215 144 214 106 216
-216 287 215 85 217
-217 266 48 216 218
-218 169 27 217 219
-219 110 220 148 218
-220 89 221 291 219
-221 220 222 270 52
-222 221 223 173 31
-223 222 114 224 152
-224 223 93 225 295
-225 56 224 226 274
-226 177 35 225 227
-227 156 226 118 228
-228 299 227 97 229
-229 278 60 228 230
-230 121 231 39 229
-231 232 160 62 230
-232 231 243 101 233
-233 232 234 4 282
-234 233 125 235 43
-235 66 234 236 164
-236 235 247 105 237
-237 286 236 238 8
-238 47 237 129 239
-239 168 70 238 240
-240 181 239 251 109
-241 242 300 50 72
-242 111 243 193 241
-243 242 232 134 244
-244 243 245 15 173
-245 244 246 54 76
-246 245 115 247 197
-247 246 236 138 248
-248 177 247 249 19
-249 58 80 248 250
-250 201 249 119 251
-251 250 240 142 252
-252 121 253 23 251
-253 254 2 84 252
-254 253 255 205 63
-255 254 146 256 184
-256 255 125 257 27
-257 88 256 258 6
-258 209 67 257 259
-259 188 258 150 260
-260 259 129 261 31
-261 92 260 262 10
-262 213 71 261 263
-263 154 264 192 262
-264 133 265 35 263
-265 264 266 14 96
-266 265 267 217 75
-267 266 158 268 196
-268 267 137 269 39
-269 100 268 270 18
-270 221 79 269 271
-271 200 270 162 272
-272 271 141 273 43
-273 22 104 272 274
-274 275 225 83 273
-275 166 276 204 274
-276 275 145 277 47
-277 276 278 26 108
-278 277 279 229 87
-279 278 170 280 208
-280 279 149 281 51
-281 112 280 282 30
-282 233 91 281 283
-283 212 282 174 284
-284 55 283 153 285
-285 286 34 116 284
-286 287 237 95 285
-287 286 178 288 216
-288 287 157 289 59
-289 288 290 38 120
-290 99 289 181 291
-291 220 122 290 292
-292 3 291 161 293
-293 292 294 42 64
-294 103 293 185 295
-295 224 126 294 296
-296 165 297 7 295
-297 298 46 68 296
-298 297 189 299 107
-299 298 300 228 130
-300 11 299 169 241
0

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