Graph forms
for C4 [ 300, 16 ] = MSZ(20,15,9,2)
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On this page are computer-accessible forms for the graph C4[ 300, 16 ] =
MSZ(20,15,9,2).
(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}, {278, 279}, {276, 277},
{274, 275}, {272, 273}, {270, 271}, {268, 269}, {266, 267}, {264, 265}, {262,
263}, {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}, {126, 127}, {124, 125}, {122, 123}, {118, 119}, {116, 117}, {114, 115},
{112, 113}, {110, 111}, {108, 109}, {106, 107}, {104, 105}, {102, 103}, {98,
99}, {96, 97}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {86, 87}, {84, 85}, {82,
83}, {78, 79}, {76, 77}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15},
{16, 17}, {18, 19}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33},
{34, 35}, {36, 37}, {38, 39}, {42, 43}, {44, 45}, {46, 47}, {48, 49}, {50, 51},
{52, 53}, {54, 55}, {56, 57}, {58, 59}, {62, 63}, {64, 65}, {66, 67}, {68, 69},
{70, 71}, {72, 73}, {74, 75}, {128, 129}, {130, 131}, {132, 133}, {134, 135},
{136, 137}, {138, 139}, {142, 143}, {144, 145}, {146, 147}, {148, 149}, {150,
151}, {152, 153}, {154, 155}, {156, 157}, {158, 159}, {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}, {202, 203}, {204, 205}, {206, 207}, {208,
209}, {210, 211}, {212, 213}, {214, 215}, {216, 217}, {218, 219}, {222, 223},
{224, 225}, {226, 227}, {228, 229}, {230, 231}, {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}, {125, 126}, {121, 122}, {117, 118}, {113, 114}, {109,
110}, {105, 106}, {101, 102}, {97, 98}, {93, 94}, {89, 90}, {85, 86}, {81, 82},
{77, 78}, {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}, {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}, {213, 214}, {217, 218}, {221,
222}, {225, 226}, {229, 230}, {3, 4}, {299, 300}, {291, 292}, {283, 284}, {275,
276}, {267, 268}, {259, 260}, {251, 252}, {243, 244}, {235, 236}, {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}, {131, 132},
{139, 140}, {147, 148}, {155, 156}, {163, 164}, {171, 172}, {179, 180}, {187,
188}, {195, 196}, {203, 204}, {211, 212}, {219, 220}, {227, 228}, {16, 25},
{276, 285}, {272, 281}, {260, 269}, {256, 265}, {240, 249}, {116, 125}, {112,
121}, {100, 109}, {96, 105}, {80, 89}, {20, 29}, {32, 41}, {36, 45}, {52, 61},
{132, 141}, {160, 169}, {176, 185}, {180, 189}, {192, 201}, {196, 205}, {212,
221}, {7, 8}, {295, 296}, {279, 280}, {263, 264}, {247, 248}, {231, 232}, {119,
120}, {103, 104}, {87, 88}, {23, 24}, {39, 40}, {55, 56}, {71, 72}, {135, 136},
{151, 152}, {167, 168}, {183, 184}, {199, 200}, {215, 216}, {1, 20}, {41, 60},
{161, 180}, {201, 220}, {12, 21}, {236, 245}, {232, 241}, {76, 85}, {40, 49},
{72, 81}, {136, 145}, {140, 149}, {172, 181}, {200, 209}, {64, 93}, {261, 280},
{101, 120}, {128, 157}, {224, 253}, {15, 16}, {271, 272}, {257, 286}, {239,
240}, {111, 112}, {97, 126}, {79, 80}, {33, 62}, {47, 48}, {143, 144}, {175,
176}, {193, 222}, {207, 208}, {4, 33}, {268, 297}, {84, 113}, {28, 57}, {68,
97}, {148, 177}, {204, 233}, {13, 42}, {93, 122}, {77, 106}, {133, 162}, {157,
186}, {197, 226}, {213, 242}, {8, 37}, {264, 293}, {88, 117}, {24, 53}, {141,
160}, {221, 240}, {73, 102}, {137, 166}, {153, 182}, {217, 246}, {1, 50}, {5,
54}, {9, 58}, {65, 114}, {69, 118}, {129, 178}, {141, 190}, {201, 250}, {205,
254}, {81, 100}, {281, 300}, {92, 101}, {280, 289}, {152, 161}, {156, 165},
{216, 225}, {220, 229}, {21, 40}, {144, 173}, {208, 237}, {17, 46}, {287, 288},
{95, 96}, {31, 32}, {159, 160}, {223, 224}, {18, 87}, {34, 103}, {58, 127},
{138, 207}, {154, 223}, {178, 247}, {38, 107}, {54, 123}, {134, 203}, {21, 70},
{25, 74}, {29, 78}, {49, 98}, {61, 110}, {145, 194}, {149, 198}, {181, 230},
{185, 234}, {189, 238}, {2, 91}, {6, 95}, {130, 219}, {162, 251}, {166, 255},
{14, 83}, {174, 243}, {44, 73}, {164, 193}, {188, 217}, {37, 66}, {53, 82},
{173, 202}, {10, 99}, {26, 115}, {30, 119}, {142, 231}, {61, 80}, {168, 197},
{184, 213}, {57, 86}, {41, 90}, {45, 94}, {161, 210}, {165, 214}, {169, 218},
{22, 111}, {56, 65}, {60, 69}, {146, 235}, {150, 239}, {48, 77}, {158, 227},
{181, 200}, {63, 64}, {177, 206}, {191, 192}, {12, 143}, {120, 251}, {116, 247},
{112, 243}, {100, 231}, {96, 227}, {92, 223}, {80, 211}, {76, 207}, {16, 147},
{20, 151}, {32, 163}, {36, 167}, {40, 171}, {52, 183}, {56, 187}, {60, 191},
{72, 203}, {8, 159}, {104, 255}, {64, 215}, {35, 184}, {99, 248}, {39, 188}, {4,
155}, {68, 219}, {42, 131}, {122, 211}, {110, 199}, {106, 195}, {46, 135}, {62,
151}, {126, 215}, {15, 164}, {95, 244}, {79, 228}, {75, 224}, {3, 172}, {83,
252}, {28, 179}, {67, 236}, {7, 176}, {88, 239}, {24, 175}, {71, 240}, {50,
139}, {19, 168}, {11, 180}, {84, 235}, {74, 143}, {114, 183}, {98, 167}, {118,
187}, {81, 130}, {125, 174}, {121, 170}, {89, 138}, {85, 134}, {11, 222}, {35,
246}, {23, 192}, {31, 200}, {63, 232}, {66, 155}, {102, 191}, {70, 159}, {39,
250}, {78, 147}, {27, 196}, {108, 137}, {124, 153}, {117, 146}, {3, 234}, {90,
179}, {7, 238}, {23, 254}, {59, 208}, {15, 226}, {104, 133}, {31, 242}, {44,
195}, {51, 220}, {101, 150}, {109, 158}, {105, 154}, {19, 230}, {121, 140}, {47,
216}, {48, 199}, {82, 171}, {120, 129}, {86, 175}, {55, 204}, {94, 163}, {43,
212}, {113, 142}, {127, 128}, {14, 265}, {30, 281}, {38, 289}, {10, 261}, {13,
284}, {2, 273}, {6, 277}, {27, 258}, {63, 294}, {18, 269}, {1, 292}, {9, 300},
{5, 296}, {17, 288}, {22, 293}, {26, 297}, {51, 262}, {59, 270}, {43, 274}, {47,
278}, {55, 266}, {34, 285}, {75, 286}, {87, 256}, {127, 296}, {71, 282}, {91,
260}, {123, 292}, {67, 298}, {79, 290}, {108, 259}, {124, 275}, {103, 272},
{111, 280}, {115, 264}, {119, 268}, {107, 276}, {132, 263}, {136, 267}, {140,
271}, {152, 283}, {156, 287}, {160, 291}, {128, 279}, {135, 284}, {170, 259},
{186, 275}, {190, 279}, {139, 288}, {131, 300}, {144, 295}, {182, 271}, {148,
299}, {194, 263}, {218, 287}, {198, 267}, {214, 283}, {209, 258}, {249, 298},
{245, 294}, {241, 290}, {221, 270}, {228, 257}, {244, 273}, {237, 266}, {253,
282}, {202, 291}, {206, 295}, {248, 277}, {233, 262}, {225, 274}, {229, 278},
{241, 260}, {210, 299}, {252, 261}, {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,
42, 83, 164, 25, 46, 87, 168, 29, 50, 91, 172, 33, 54, 95, 176, 37, 58, 99,
180)(22, 43, 84, 165, 26, 47, 88, 169, 30, 51, 92, 173, 34, 55, 96, 177, 38, 59,
100, 161)(23, 44, 85, 166, 27, 48, 89, 170, 31, 52, 93, 174, 35, 56, 97, 178,
39, 60, 81, 162)(24, 45, 86, 167, 28, 49, 90, 171, 32, 53, 94, 175, 36, 57, 98,
179, 40, 41, 82, 163)(61, 122, 243, 184, 65, 126, 247, 188, 69, 130, 251, 192,
73, 134, 255, 196, 77, 138, 259, 200)(62, 123, 244, 185, 66, 127, 248, 189, 70,
131, 252, 193, 74, 135, 256, 197, 78, 139, 260, 181)(63, 124, 245, 186, 67, 128,
249, 190, 71, 132, 253, 194, 75, 136, 257, 198, 79, 140, 241, 182)(64, 125, 246,
187, 68, 129, 250, 191, 72, 133, 254, 195, 76, 137, 258, 199, 80, 121, 242,
183)(101, 202, 103, 204, 105, 206, 107, 208, 109, 210, 111, 212, 113, 214, 115,
216, 117, 218, 119, 220)(102, 203, 104, 205, 106, 207, 108, 209, 110, 211, 112,
213, 114, 215, 116, 217, 118, 219, 120, 201)(141, 282, 263, 224, 145, 286, 267,
228, 149, 290, 271, 232, 153, 294, 275, 236, 157, 298, 279, 240)(142, 283, 264,
225, 146, 287, 268, 229, 150, 291, 272, 233, 154, 295, 276, 237, 158, 299, 280,
221)(143, 284, 265, 226, 147, 288, 269, 230, 151, 292, 273, 234, 155, 296, 277,
238, 159, 300, 261, 222)(144, 285, 266, 227, 148, 289, 270, 231, 152, 293, 274,
235, 156, 297, 278, 239, 160, 281, 262, 223) (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 **************
b: (2, 50)(3, 139)(4, 288)(5, 17)(6, 46)(7, 135)(8, 284)(9, 13)(10, 42)(11,
131)(12, 300)(14, 58)(15, 127)(16, 296)(18, 54)(19, 123)(20, 292)(21, 281)(22,
30)(23, 119)(24, 268)(25, 297)(27, 115)(28, 264)(29, 293)(31, 111)(32, 280)(33,
289)(34, 38)(35, 107)(36, 276)(37, 285)(39, 103)(40, 272)(41, 261)(43, 99)(44,
248)(45, 277)(47, 95)(48, 244)(49, 273)(51, 91)(52, 260)(53, 269)(55, 87)(56,
256)(57, 265)(59, 83)(60, 252)(61, 241)(62, 290)(63, 79)(64, 228)(65, 257)(66,
286)(67, 75)(68, 224)(69, 253)(70, 282)(72, 240)(73, 249)(74, 298)(76, 236)(77,
245)(78, 294)(80, 232)(81, 221)(82, 270)(84, 208)(85, 237)(86, 266)(88, 204)(89,
233)(90, 262)(92, 220)(93, 229)(94, 278)(96, 216)(97, 225)(98, 274)(100,
212)(101, 201)(102, 250)(104, 188)(105, 217)(106, 246)(108, 184)(109, 213)(110,
242)(112, 200)(113, 209)(114, 258)(116, 196)(117, 205)(118, 254)(120, 192)(121,
181)(122, 230)(124, 168)(125, 197)(126, 226)(128, 164)(129, 193)(130, 222)(132,
180)(133, 189)(134, 238)(136, 176)(137, 185)(138, 234)(140, 172)(141, 161)(142,
210)(143, 299)(144, 148)(145, 177)(146, 206)(147, 295)(149, 173)(150, 202)(151,
291)(152, 160)(153, 169)(154, 218)(155, 287)(157, 165)(158, 214)(159, 283)(162,
190)(163, 279)(166, 186)(167, 275)(170, 182)(171, 271)(174, 198)(175, 267)(178,
194)(179, 263)(183, 259)(187, 255)(191, 251)(195, 247)(199, 243)(203, 239)(207,
235)(211, 231)(215, 227)(219, 223)
C4[ 300, 16 ]
300
-1 2 50 292 20
-2 1 3 91 273
-3 2 234 4 172
-4 33 155 3 5
-5 4 6 54 296
-6 277 5 7 95
-7 176 6 238 8
-8 37 159 7 9
-9 58 300 8 10
-10 11 99 261 9
-11 12 222 180 10
-12 11 143 13 21
-13 12 14 42 284
-14 265 13 15 83
-15 14 16 226 164
-16 25 15 147 17
-17 46 288 16 18
-18 269 17 19 87
-19 168 18 20 230
-20 1 29 19 151
-21 22 12 70 40
-22 23 111 293 21
-23 22 254 24 192
-24 23 25 53 175
-25 24 26 16 74
-26 297 25 27 115
-27 26 258 28 196
-28 57 179 27 29
-29 78 28 30 20
-30 281 29 31 119
-31 242 200 30 32
-32 33 41 31 163
-33 34 4 62 32
-34 33 35 103 285
-35 34 36 246 184
-36 45 35 167 37
-37 66 36 38 8
-38 289 37 39 107
-39 188 38 40 250
-40 49 39 171 21
-41 90 60 42 32
-42 13 41 43 131
-43 44 212 42 274
-44 45 73 195 43
-45 44 46 36 94
-46 45 47 135 17
-47 46 278 48 216
-48 77 199 47 49
-49 48 50 40 98
-50 1 49 51 139
-51 220 50 52 262
-52 61 51 183 53
-53 24 82 52 54
-54 55 123 5 53
-55 56 266 204 54
-56 55 187 57 65
-57 56 58 28 86
-58 57 59 127 9
-59 58 60 270 208
-60 69 59 191 41
-61 110 80 62 52
-62 33 61 63 151
-63 232 62 294 64
-64 93 215 63 65
-65 66 56 114 64
-66 67 155 37 65
-67 66 298 68 236
-68 67 69 97 219
-69 68 70 60 118
-70 69 71 159 21
-71 70 72 282 240
-72 81 71 203 73
-73 44 102 72 74
-74 143 25 73 75
-75 286 224 74 76
-76 77 85 75 207
-77 78 48 106 76
-78 77 79 147 29
-79 78 80 290 228
-80 89 79 211 61
-81 100 82 72 130
-82 81 83 171 53
-83 14 82 84 252
-84 113 235 83 85
-85 134 84 86 76
-86 57 85 87 175
-87 88 256 18 86
-88 89 117 239 87
-89 88 90 80 138
-90 89 91 179 41
-91 2 90 92 260
-92 101 91 223 93
-93 122 92 94 64
-94 45 93 95 163
-95 244 6 94 96
-96 105 95 227 97
-97 68 126 96 98
-98 99 167 49 97
-99 100 248 10 98
-100 99 231 81 109
-101 102 92 150 120
-102 101 103 191 73
-103 34 102 104 272
-104 133 255 103 105
-105 154 104 106 96
-106 77 105 107 195
-107 276 38 106 108
-108 137 259 107 109
-109 110 100 158 108
-110 111 199 61 109
-111 22 110 112 280
-112 121 111 243 113
-113 112 114 84 142
-114 113 115 183 65
-115 264 26 114 116
-116 125 115 247 117
-117 88 146 116 118
-118 187 69 117 119
-119 268 30 118 120
-120 101 129 119 251
-121 122 112 170 140
-122 121 123 211 93
-123 122 124 292 54
-124 275 123 125 153
-125 124 126 116 174
-126 125 127 215 97
-127 58 126 128 296
-128 157 279 127 129
-129 178 128 130 120
-130 81 129 131 219
-131 132 300 42 130
-132 133 141 131 263
-133 132 134 104 162
-134 133 135 203 85
-135 46 134 136 284
-136 145 135 267 137
-137 166 136 138 108
-138 89 137 139 207
-139 288 50 138 140
-140 121 149 139 271
-141 132 190 160 142
-142 143 231 113 141
-143 12 144 74 142
-144 143 145 173 295
-145 144 146 136 194
-146 145 147 235 117
-147 78 146 16 148
-148 177 299 147 149
-149 198 148 150 140
-150 101 149 151 239
-151 62 150 20 152
-152 161 151 283 153
-153 154 124 182 152
-154 155 223 105 153
-155 66 154 156 4
-156 165 155 287 157
-157 156 158 128 186
-158 157 159 227 109
-159 70 158 160 8
-160 169 159 291 141
-161 210 180 162 152
-162 133 161 163 251
-163 94 162 32 164
-164 165 15 193 163
-165 166 156 214 164
-166 165 167 255 137
-167 166 36 168 98
-168 167 169 19 197
-169 168 170 160 218
-170 121 169 171 259
-171 82 170 40 172
-172 3 181 171 173
-173 144 202 172 174
-174 243 125 173 175
-175 176 24 86 174
-176 177 7 185 175
-177 176 178 148 206
-178 177 179 247 129
-179 90 178 180 28
-180 11 189 179 161
-181 200 182 172 230
-182 181 183 271 153
-183 114 182 52 184
-184 35 213 183 185
-185 176 234 184 186
-186 187 275 157 185
-187 56 188 118 186
-188 187 189 39 217
-189 188 190 180 238
-190 189 191 279 141
-191 102 190 60 192
-192 23 201 191 193
-193 222 192 194 164
-194 145 193 195 263
-195 44 106 194 196
-196 27 205 195 197
-197 198 168 226 196
-198 199 267 149 197
-199 110 198 200 48
-200 209 199 181 31
-201 220 202 192 250
-202 201 203 291 173
-203 134 202 72 204
-204 55 233 203 205
-205 254 204 206 196
-206 177 205 207 295
-207 138 206 76 208
-208 209 59 237 207
-209 210 200 258 208
-210 209 211 299 161
-211 122 210 80 212
-212 221 211 213 43
-213 242 212 214 184
-214 165 213 215 283
-215 126 214 216 64
-216 47 225 215 217
-217 188 246 216 218
-218 287 169 217 219
-219 220 68 130 218
-220 201 51 229 219
-221 222 212 270 240
-222 11 221 223 193
-223 154 222 92 224
-224 253 223 225 75
-225 224 226 216 274
-226 15 225 227 197
-227 158 226 96 228
-228 79 257 227 229
-229 220 278 228 230
-230 231 181 19 229
-231 100 232 142 230
-232 231 233 63 241
-233 232 234 204 262
-234 233 3 235 185
-235 146 234 236 84
-236 67 245 235 237
-237 266 236 238 208
-238 189 237 7 239
-239 88 150 238 240
-240 221 71 249 239
-241 242 232 290 260
-242 243 213 31 241
-243 242 112 244 174
-244 243 245 95 273
-245 244 246 236 294
-246 35 245 247 217
-247 178 246 116 248
-248 99 277 247 249
-249 298 248 250 240
-250 201 39 249 251
-251 162 250 120 252
-252 253 83 261 251
-253 254 224 282 252
-254 253 23 255 205
-255 166 254 256 104
-256 265 255 257 87
-257 286 256 258 228
-258 209 257 27 259
-259 170 258 260 108
-260 91 269 259 241
-261 280 262 10 252
-262 233 51 261 263
-263 132 264 194 262
-264 265 115 293 263
-265 264 266 14 256
-266 55 265 267 237
-267 198 266 136 268
-268 297 267 269 119
-269 268 270 18 260
-270 221 59 269 271
-271 182 270 140 272
-272 103 281 271 273
-273 2 244 272 274
-274 275 225 273 43
-275 276 124 186 274
-276 275 277 107 285
-277 276 278 6 248
-278 277 47 279 229
-279 190 278 280 128
-280 111 289 279 261
-281 300 282 30 272
-282 253 71 281 283
-283 214 282 152 284
-284 13 135 283 285
-285 286 34 276 284
-286 287 257 75 285
-287 286 156 288 218
-288 287 289 17 139
-289 288 290 38 280
-290 79 289 291 241
-291 202 290 160 292
-292 1 123 291 293
-293 22 264 292 294
-294 245 293 63 295
-295 144 206 294 296
-296 297 5 127 295
-297 298 26 268 296
-298 297 67 299 249
-299 210 298 300 148
-300 299 281 9 131
0