Graph forms
for C4 [ 320, 160 ] = UG(Cmap(640,73){16,4|5}_20)
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On this page are computer-accessible forms for the graph C4[ 320, 160 ] =
UG(Cmap(640,73){16,4|5}_20).
(I) Following is a form readable by MAGMA:
g:=Graph<320|{ {2, 3}, {292, 293}, {110, 111}, {140, 141}, {4, 6}, {209, 211},
{1, 2}, {249, 250}, {89, 90}, {169, 170}, {1, 4}, {10, 15}, {8, 13}, {1, 7},
{210, 212}, {3, 5}, {9, 14}, {306, 309}, {163, 164}, {16, 24}, {259, 267}, {193,
201}, {18, 26}, {17, 25}, {192, 201}, {20, 30}, {305, 315}, {1, 10}, {246, 253},
{7, 11}, {304, 316}, {5, 8}, {277, 280}, {247, 250}, {48, 61}, {117, 120}, {166,
171}, {180, 185}, {2, 12}, {311, 313}, {19, 29}, {6, 9}, {55, 56}, {181, 186},
{183, 184}, {3, 19}, {77, 93}, {33, 49}, {32, 48}, {4, 20}, {204, 221}, {303,
318}, {271, 286}, {228, 245}, {135, 149}, {2, 17}, {231, 244}, {199, 212}, {103,
116}, {160, 179}, {43, 63}, {302, 314}, {297, 317}, {296, 316}, {34, 55}, {42,
63}, {40, 61}, {41, 62}, {225, 246}, {72, 95}, {3, 27}, {15, 23}, {14, 22}, {13,
21}, {4, 28}, {265, 272}, {5, 31}, {291, 313}, {11, 16}, {257, 282}, {39, 60},
{35, 56}, {267, 279}, {299, 311}, {36, 57}, {294, 315}, {288, 317}, {202, 215},
{38, 59}, {12, 18}, {294, 312}, {289, 319}, {238, 240}, {37, 58}, {301, 306},
{288, 319}, {271, 272}, {64, 96}, {263, 295}, {262, 294}, {67, 99}, {66, 98},
{65, 97}, {69, 100}, {267, 298}, {206, 239}, {198, 231}, {79, 110}, {77, 108},
{75, 106}, {73, 104}, {71, 102}, {70, 100}, {278, 308}, {200, 234}, {132, 166},
{139, 169}, {70, 101}, {276, 311}, {78, 109}, {74, 105}, {131, 167}, {281, 317},
{275, 310}, {6, 32}, {279, 305}, {212, 242}, {88, 126}, {81, 119}, {7, 33},
{129, 167}, {131, 165}, {76, 107}, {282, 306}, {287, 311}, {5, 44}, {275, 314},
{273, 312}, {7, 46}, {153, 176}, {82, 120}, {269, 295}, {264, 290}, {87, 125},
{86, 124}, {83, 121}, {6, 45}, {285, 310}, {266, 289}, {154, 182}, {274, 318},
{79, 98}, {198, 235}, {159, 178}, {84, 122}, {85, 123}, {72, 103}, {78, 97},
{31, 47}, {146, 162}, {156, 172}, {210, 227}, {218, 232}, {23, 36}, {261, 310},
{207, 252}, {27, 40}, {272, 292}, {22, 35}, {202, 255}, {68, 113}, {30, 43},
{28, 41}, {137, 191}, {21, 34}, {29, 42}, {83, 107}, {260, 316}, {84, 108},
{128, 184}, {129, 185}, {130, 186}, {133, 188}, {268, 309}, {135, 190}, {8, 50},
{256, 314}, {199, 253}, {198, 252}, {12, 54}, {9, 51}, {134, 189}, {286, 293},
{194, 249}, {271, 307}, {24, 37}, {284, 289}, {26, 39}, {10, 52}, {208, 238},
{197, 251}, {196, 250}, {11, 53}, {17, 46}, {80, 111}, {25, 38}, {132, 187}, {9,
72}, {11, 74}, {154, 219}, {158, 223}, {161, 224}, {178, 243}, {156, 222}, {10,
73}, {16, 84}, {19, 87}, {18, 86}, {17, 85}, {144, 212}, {145, 213}, {147, 214},
{164, 225}, {47, 105}, {155, 221}, {12, 75}, {170, 226}, {172, 228}, {173, 229},
{129, 203}, {138, 192}, {139, 193}, {168, 226}, {169, 227}, {174, 228}, {175,
229}, {147, 216}, {168, 227}, {20, 88}, {150, 218}, {148, 217}, {132, 202},
{137, 199}, {138, 196}, {158, 208}, {8, 71}, {191, 240}, {27, 75}, {190, 238},
{189, 237}, {188, 236}, {187, 235}, {146, 194}, {143, 222}, {40, 122}, {184,
234}, {28, 73}, {50, 103}, {167, 241}, {165, 242}, {37, 125}, {44, 117}, {140,
213}, {45, 118}, {283, 320}, {170, 241}, {179, 232}, {13, 81}, {15, 83}, {14,
82}, {143, 211}, {164, 248}, {181, 233}, {140, 209}, {150, 200}, {190, 224},
{287, 320}, {62, 94}, {63, 95}, {58, 91}, {190, 223}, {60, 93}, {149, 244}, {20,
118}, {189, 223}, {16, 115}, {185, 218}, {57, 90}, {136, 235}, {18, 116}, {54,
80}, {19, 117}, {130, 228}, {59, 92}, {179, 219}, {21, 127}, {43, 64}, {47, 68},
{128, 235}, {55, 91}, {176, 220}, {177, 221}, {44, 65}, {46, 67}, {55, 89}, {45,
66}, {174, 222}, {173, 220}, {178, 195}, {154, 233}, {307, 320}, {48, 69}, {49,
70}, {51, 68}, {136, 240}, {134, 255}, {52, 78}, {53, 79}, {151, 237}, {177,
203}, {145, 237}, {180, 200}, {13, 112}, {15, 114}, {50, 76}, {51, 77}, {14,
113}, {168, 215}, {60, 191}, {88, 219}, {114, 246}, {115, 247}, {65, 196}, {71,
193}, {66, 197}, {64, 201}, {102, 239}, {39, 171}, {116, 248}, {119, 251}, {82,
220}, {94, 208}, {46, 161}, {83, 220}, {126, 241}, {120, 232}, {110, 255}, {94,
205}, {43, 191}, {104, 252}, {32, 181}, {22, 128}, {31, 137}, {30, 136}, {23,
129}, {33, 182}, {35, 187}, {79, 215}, {78, 214}, {103, 254}, {24, 130}, {29,
135}, {28, 134}, {25, 131}, {26, 132}, {98, 252}, {27, 133}, {70, 217}, {87,
243}, {102, 192}, {126, 216}, {51, 148}, {40, 128}, {25, 176}, {32, 138}, {33,
139}, {26, 177}, {31, 180}, {30, 179}, {75, 230}, {73, 231}, {29, 178}, {59,
136}, {119, 195}, {24, 175}, {21, 172}, {96, 217}, {23, 174}, {22, 173}, {48,
143}, {112, 207}, {80, 144}, {63, 254}, {52, 246}, {53, 247}, {111, 173}, {74,
137}, {108, 175}, {49, 245}, {58, 254}, {107, 174}, {127, 183}, {54, 248}, {95,
145}, {94, 144}, {81, 159}, {84, 133}, {92, 141}, {77, 159}, {118, 164}, {119,
165}, {93, 142}, {115, 160}, {123, 168}, {38, 242}, {59, 239}, {36, 241}, {89,
140}, {87, 130}, {124, 169}, {126, 171}, {116, 162}, {117, 163}, {125, 171},
{89, 142}, {125, 170}, {69, 157}, {101, 188}, {41, 243}, {122, 167}, {42, 244},
{121, 166}, {34, 194}, {39, 199}, {38, 198}, {37, 197}, {36, 196}, {35, 195},
{121, 153}, {41, 200}, {42, 201}, {96, 131}, {47, 204}, {124, 152}, {44, 202},
{54, 208}, {45, 203}, {114, 148}, {115, 149}, {127, 153}, {121, 145}, {122,
146}, {123, 151}, {112, 157}, {114, 159}, {76, 162}, {112, 158}, {113, 158},
{34, 210}, {105, 153}, {104, 152}, {99, 147}, {106, 154}, {100, 149}, {102,
151}, {109, 156}, {82, 160}, {96, 146}, {110, 156}, {71, 180}, {101, 150}, {111,
155}, {109, 155}, {101, 157}, {57, 192}, {52, 206}, {65, 187}, {53, 207}, {66,
185}, {49, 205}, {74, 182}, {50, 207}, {72, 181}, {80, 175}, {62, 292}, {62,
264}, {56, 271}, {61, 261}, {60, 262}, {61, 263}, {56, 259}, {57, 260}, {58,
261}, {67, 263}, {106, 303}, {91, 285}, {76, 267}, {64, 265}, {69, 268}, {67,
266}, {97, 299}, {120, 306}, {100, 296}, {68, 266}, {98, 300}, {97, 303}, {99,
304}, {88, 270}, {85, 268}, {107, 305}, {86, 269}, {106, 305}, {81, 269}, {85,
264}, {92, 258}, {123, 275}, {124, 276}, {118, 287}, {108, 262}, {105, 260},
{127, 274}, {104, 262}, {90, 296}, {92, 302}, {86, 293}, {113, 258}, {90, 300},
{95, 297}, {93, 299}, {91, 301}, {109, 277}, {99, 284}, {150, 277}, {186, 313},
{161, 295}, {160, 296}, {161, 297}, {189, 308}, {162, 302}, {182, 314}, {138,
263}, {141, 256}, {142, 259}, {166, 297}, {133, 277}, {183, 294}, {177, 293},
{135, 274}, {163, 309}, {165, 319}, {155, 256}, {163, 319}, {139, 278}, {147,
270}, {148, 265}, {157, 258}, {152, 312}, {172, 269}, {151, 309}, {188, 287},
{183, 260}, {141, 312}, {134, 304}, {142, 313}, {176, 264}, {248, 320}, {144,
298}, {186, 257}, {143, 307}, {184, 261}, {152, 295}, {209, 273}, {210, 274},
{225, 288}, {216, 282}, {232, 298}, {243, 304}, {249, 317}, {211, 283}, {219,
275}, {217, 273}, {216, 272}, {253, 308}, {211, 281}, {233, 291}, {203, 256},
{206, 258}, {204, 257}, {214, 280}, {234, 292}, {234, 315}, {250, 299}, {222,
268}, {233, 315}, {193, 276}, {221, 266}, {253, 298}, {251, 300}, {249, 302},
{247, 288}, {230, 318}, {218, 259}, {251, 289}, {205, 273}, {255, 291}, {254,
290}, {224, 318}, {209, 270}, {204, 301}, {215, 310}, {213, 308}, {206, 303},
{244, 279}, {245, 278}, {197, 290}, {214, 316}, {242, 280}, {229, 270}, {240,
284}, {194, 301}, {230, 265}, {205, 290}, {195, 307}, {236, 284}, {236, 285},
{239, 286}, {237, 286}, {238, 285}, {245, 257}, {226, 279}, {225, 278}, {236,
276}, {213, 300}, {226, 283}, {224, 281}, {227, 280}, {223, 291}, {231, 283},
{230, 282}, {229, 281} }>;
(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, 10)(4, 12)(5, 15)(6, 18)(7, 17)(8, 23)(9, 26)(11, 25)(13, 36)(14,
39)(16, 38)(19, 52)(20, 54)(21, 57)(22, 60)(24, 59)(27, 73)(28, 75)(29, 78)(30,
80)(31, 83)(32, 86)(33, 85)(34, 90)(35, 93)(37, 92)(40, 104)(41, 106)(42,
109)(43, 111)(44, 114)(45, 116)(47, 121)(48, 124)(49, 123)(50, 129)(51, 132)(53,
131)(55, 89)(56, 142)(58, 141)(61, 152)(62, 154)(63, 155)(64, 110)(65, 159)(66,
162)(67, 161)(68, 166)(69, 169)(70, 168)(71, 174)(72, 177)(74, 176)(76, 185)(77,
187)(79, 96)(81, 196)(82, 199)(84, 198)(87, 206)(88, 208)(91, 140)(94, 219)(95,
221)(97, 178)(98, 146)(99, 224)(100, 227)(101, 226)(102, 228)(103, 203)(105,
153)(107, 180)(108, 235)(112, 241)(113, 171)(115, 242)(117, 246)(118, 248)(119,
250)(120, 253)(122, 252)(125, 258)(126, 158)(127, 260)(128, 262)(130, 239)(133,
231)(134, 230)(135, 214)(136, 175)(137, 220)(138, 269)(139, 268)(143, 276)(144,
179)(145, 204)(147, 190)(148, 202)(149, 280)(150, 279)(151, 245)(156, 201)(157,
170)(160, 212)(163, 225)(165, 247)(167, 207)(172, 192)(173, 191)(181, 293)(182,
264)(184, 294)(186, 286)(188, 283)(189, 282)(193, 222)(194, 300)(195, 299)(197,
302)(200, 305)(205, 275)(209, 285)(210, 296)(211, 236)(213, 301)(215, 217)(216,
223)(218, 267)(229, 240)(232, 298)(233, 292)(234, 315)(237, 257)(238, 270)(243,
303)(244, 277)(249, 251)(254, 256)(255, 265)(261, 312)(263, 295)(266, 297)(271,
313)(272, 291)(273, 310)(274, 316)(278, 309)(281, 284)(287, 320)(288, 319)(289,
317)(290, 314)(304, 318)(306, 308)(307, 311) (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, 4, 7, 10)(3, 6, 11, 15)(5, 9, 16, 23)(8, 14, 24, 36)(12, 20, 33, 52)(13,
22, 37, 57)(17, 28, 46, 73)(18, 30, 49, 78)(19, 32, 53, 83)(21, 35, 58, 90)(25,
41, 67, 104)(26, 43, 70, 109)(27, 45, 74, 114)(29, 48, 79, 121)(31, 51, 84,
129)(34, 56, 91, 89)(38, 62, 99, 152)(39, 64, 101, 155)(40, 66, 105, 159)(42,
69, 110, 166)(44, 72, 115, 174)(47, 77, 122, 185)(50, 82, 130, 196)(54, 88, 139,
206)(59, 94, 147, 124)(60, 96, 150, 221)(61, 98, 153, 178)(63, 100, 156,
132)(65, 103, 160, 228)(68, 108, 167, 180)(71, 113, 175, 241)(75, 118, 182,
246)(76, 120, 186, 250)(80, 126, 193, 258)(81, 128, 197, 260)(85, 134, 161,
231)(86, 136, 205, 214)(87, 138, 207, 220)(92, 144, 216, 276)(93, 146, 218,
204)(95, 149, 222, 202)(97, 116, 179, 245)(102, 158, 229, 170)(106, 164, 154,
225)(107, 117, 181, 247)(111, 171, 201, 157)(112, 173, 125, 192)(119, 184, 251,
183)(123, 189, 224, 283)(127, 195, 261, 300)(131, 200, 266, 262)(133, 203, 137,
148)(135, 143, 215, 145)(140, 210, 271, 285)(141, 212, 272, 236)(142, 194, 259,
301)(151, 223, 281, 226)(162, 232, 257, 299)(163, 233, 288, 305)(165, 234, 289,
294)(168, 237, 190, 211)(169, 239, 208, 270)(172, 187, 254, 296)(176, 243, 263,
252)(177, 191, 217, 277)(188, 256, 199, 265)(198, 264, 304, 295)(209, 227, 286,
238)(213, 274, 307, 310)(219, 278, 303, 248)(230, 287, 314, 253)(235, 290, 316,
269)(240, 273, 280, 293)(242, 292, 284, 312)(244, 268, 255, 297)(249, 267, 306,
313)(275, 308, 318, 320)(279, 309, 291, 317)(282, 311, 302, 298)(315, 319)
C4[ 320, 160 ]
320
-1 2 4 7 10
-2 1 12 3 17
-3 2 5 27 19
-4 1 6 28 20
-5 44 3 8 31
-6 45 4 9 32
-7 11 33 1 46
-8 13 5 71 50
-9 14 6 72 51
-10 1 15 73 52
-11 16 7 74 53
-12 2 18 75 54
-13 112 81 8 21
-14 22 113 82 9
-15 23 114 83 10
-16 11 24 115 84
-17 2 46 25 85
-18 12 26 116 86
-19 3 29 117 87
-20 88 4 30 118
-21 34 13 127 172
-22 35 14 128 173
-23 36 15 129 174
-24 37 16 130 175
-25 176 38 17 131
-26 132 177 39 18
-27 133 3 40 75
-28 134 4 73 41
-29 178 135 19 42
-30 179 136 20 43
-31 47 180 5 137
-32 48 181 6 138
-33 49 182 7 139
-34 55 210 194 21
-35 22 187 56 195
-36 23 57 196 241
-37 24 58 125 197
-38 198 242 25 59
-39 199 26 60 171
-40 122 27 61 128
-41 243 200 28 62
-42 244 201 29 63
-43 191 30 63 64
-44 202 5 117 65
-45 66 203 6 118
-46 67 17 7 161
-47 68 105 204 31
-48 143 69 61 32
-49 33 245 70 205
-50 103 8 207 76
-51 77 68 148 9
-52 78 246 206 10
-53 11 79 247 207
-54 12 80 248 208
-55 34 56 89 91
-56 55 35 259 271
-57 90 36 192 260
-58 254 91 37 261
-59 92 136 38 239
-60 191 93 39 262
-61 48 40 261 263
-62 264 94 292 41
-63 254 95 42 43
-64 265 201 96 43
-65 44 187 97 196
-66 45 185 98 197
-67 99 46 266 263
-68 266 47 113 51
-69 100 157 48 268
-70 100 101 49 217
-71 102 180 193 8
-72 103 181 95 9
-73 231 104 28 10
-74 11 137 105 182
-75 12 27 106 230
-76 267 50 107 162
-77 93 159 51 108
-78 214 52 97 109
-79 110 215 53 98
-80 111 144 54 175
-81 13 159 269 119
-82 220 14 160 120
-83 121 220 15 107
-84 122 133 16 108
-85 264 123 268 17
-86 124 269 18 293
-87 243 125 19 130
-88 126 270 20 219
-89 55 90 140 142
-90 89 57 300 296
-91 55 58 301 285
-92 59 258 302 141
-93 77 299 60 142
-94 144 62 205 208
-95 297 145 72 63
-96 146 217 64 131
-97 78 299 303 65
-98 66 79 300 252
-99 67 147 304 284
-100 69 70 149 296
-101 188 157 70 150
-102 71 192 151 239
-103 254 50 72 116
-104 73 152 262 252
-105 47 260 74 153
-106 154 303 305 75
-107 83 305 174 76
-108 77 84 262 175
-109 78 155 156 277
-110 111 79 156 255
-111 110 155 80 173
-112 13 157 158 207
-113 68 14 158 258
-114 15 246 148 159
-115 16 247 149 160
-116 103 248 18 162
-117 44 19 163 120
-118 45 287 20 164
-119 165 81 195 251
-120 232 82 117 306
-121 166 145 83 153
-122 167 146 40 84
-123 275 168 85 151
-124 276 169 86 152
-125 37 170 171 87
-126 88 171 216 241
-127 183 21 153 274
-128 22 235 40 184
-129 23 167 203 185
-130 24 228 87 186
-131 165 167 25 96
-132 187 166 26 202
-133 188 277 27 84
-134 189 255 28 304
-135 190 149 29 274
-136 59 235 30 240
-137 199 191 74 31
-138 192 196 32 263
-139 33 278 169 193
-140 209 89 213 141
-141 256 92 312 140
-142 89 93 313 259
-143 211 222 48 307
-144 298 80 212 94
-145 121 213 237 95
-146 122 194 96 162
-147 99 214 270 216
-148 265 114 51 217
-149 100 244 135 115
-150 101 200 277 218
-151 309 123 102 237
-152 124 312 104 295
-153 121 176 105 127
-154 233 182 106 219
-155 111 221 256 109
-156 110 222 172 109
-157 101 112 69 258
-158 112 113 223 208
-159 77 178 81 114
-160 179 82 115 296
-161 297 46 224 295
-162 146 302 116 76
-163 319 309 117 164
-164 225 248 118 163
-165 242 319 119 131
-166 121 132 297 171
-167 122 129 131 241
-168 123 215 226 227
-169 124 170 139 227
-170 125 169 226 241
-171 166 125 126 39
-172 156 269 228 21
-173 22 220 111 229
-174 23 222 107 228
-175 24 80 108 229
-176 220 264 25 153
-177 221 26 203 293
-178 243 159 29 195
-179 232 160 30 219
-180 200 71 31 185
-181 233 72 32 186
-182 33 154 314 74
-183 127 260 184 294
-184 234 128 183 261
-185 66 180 129 218
-186 257 181 313 130
-187 132 35 235 65
-188 133 287 101 236
-189 308 134 223 237
-190 135 223 224 238
-191 60 137 240 43
-192 57 102 201 138
-193 276 201 71 139
-194 34 146 301 249
-195 35 178 119 307
-196 36 138 250 65
-197 66 37 290 251
-198 231 235 38 252
-199 253 212 137 39
-200 234 180 150 41
-201 192 193 42 64
-202 44 132 255 215
-203 45 177 256 129
-204 221 47 257 301
-205 290 49 94 273
-206 258 303 52 239
-207 112 50 53 252
-208 158 94 238 54
-209 211 270 140 273
-210 34 212 227 274
-211 143 209 281 283
-212 242 144 199 210
-213 308 145 300 140
-214 78 147 280 316
-215 79 310 168 202
-216 147 126 282 272
-217 70 148 96 273
-218 232 259 150 185
-219 88 154 275 179
-220 176 82 83 173
-221 155 177 266 204
-222 143 156 268 174
-223 189 190 158 291
-224 190 281 161 318
-225 288 278 246 164
-226 168 279 170 283
-227 210 168 169 280
-228 245 172 130 174
-229 270 281 173 175
-230 265 282 75 318
-231 198 244 73 283
-232 298 179 218 120
-233 154 181 291 315
-234 200 292 315 184
-235 187 198 136 128
-236 188 276 284 285
-237 286 145 189 151
-238 190 240 208 285
-239 286 102 59 206
-240 136 191 238 284
-241 167 36 126 170
-242 165 212 38 280
-243 178 304 41 87
-244 231 279 149 42
-245 278 257 49 228
-246 253 114 225 52
-247 288 115 250 53
-248 320 116 54 164
-249 302 194 250 317
-250 299 247 249 196
-251 289 300 119 197
-252 198 104 207 98
-253 308 199 298 246
-254 58 103 290 63
-255 110 134 202 291
-256 155 203 314 141
-257 245 204 282 186
-258 113 157 92 206
-259 56 267 218 142
-260 57 105 183 316
-261 310 58 61 184
-262 60 104 294 108
-263 67 61 138 295
-264 176 290 62 85
-265 148 272 64 230
-266 67 221 68 289
-267 298 279 259 76
-268 309 222 69 85
-269 81 172 86 295
-270 88 209 147 229
-271 286 56 272 307
-272 265 292 216 271
-273 209 312 205 217
-274 210 135 127 318
-275 123 310 314 219
-276 124 311 236 193
-277 133 280 150 109
-278 308 245 225 139
-279 244 267 226 305
-280 242 277 214 227
-281 211 224 229 317
-282 257 216 306 230
-283 231 320 211 226
-284 99 289 236 240
-285 310 91 236 238
-286 237 271 293 239
-287 188 320 311 118
-288 319 225 247 317
-289 319 266 251 284
-290 264 254 205 197
-291 233 255 223 313
-292 234 62 293 272
-293 286 177 292 86
-294 312 183 315 262
-295 269 161 152 263
-296 100 90 160 316
-297 166 95 161 317
-298 253 144 232 267
-299 311 93 250 97
-300 90 213 251 98
-301 91 204 194 306
-302 92 314 249 162
-303 106 206 97 318
-304 99 243 134 316
-305 279 106 315 107
-306 309 301 282 120
-307 143 320 271 195
-308 253 189 278 213
-309 268 151 163 306
-310 275 215 261 285
-311 276 287 299 313
-312 294 141 152 273
-313 311 291 142 186
-314 275 256 302 182
-315 233 234 294 305
-316 214 260 304 296
-317 297 288 281 249
-318 224 303 230 274
-319 165 288 289 163
-320 287 248 283 307
0