Graph forms
for C4 [ 264, 20 ] = KE_66(1,3,22,25,23)
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On this page are computer-accessible forms for the graph C4[ 264, 20 ] =
KE_66(1,3,22,25,23).
(I) Following is a form readable by MAGMA:
g:=Graph<264|{ {2, 3}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54,
55}, {52, 53}, {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}, {1, 2}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {5, 6}, {9, 10}, {13,
14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45,
46}, {49, 50}, {3, 4}, {59, 60}, {51, 52}, {11, 12}, {19, 20}, {27, 28}, {35,
36}, {43, 44}, {7, 8}, {55, 56}, {23, 24}, {39, 40}, {128, 150}, {129, 151},
{200, 223}, {232, 255}, {224, 247}, {199, 222}, {231, 254}, {229, 252}, {227,
250}, {225, 248}, {130, 152}, {131, 153}, {226, 249}, {230, 253}, {132, 154},
{15, 16}, {228, 251}, {47, 48}, {201, 224}, {223, 246}, {221, 244}, {219, 242},
{217, 240}, {203, 226}, {205, 228}, {207, 230}, {202, 225}, {222, 245}, {218,
241}, {212, 255}, {206, 229}, {208, 251}, {209, 252}, {211, 254}, {204, 227},
{220, 243}, {210, 253}, {199, 242}, {205, 248}, {207, 250}, {206, 249}, {216,
239}, {208, 231}, {209, 232}, {215, 238}, {213, 236}, {211, 234}, {200, 243},
{214, 237}, {210, 233}, {204, 247}, {201, 244}, {203, 246}, {31, 32}, {212,
235}, {64, 127}, {202, 245}, {5, 68}, {63, 126}, {61, 124}, {59, 122}, {57,
120}, {55, 118}, {53, 116}, {51, 114}, {7, 70}, {9, 72}, {11, 74}, {13, 76},
{15, 78}, {17, 80}, {19, 82}, {21, 84}, {23, 86}, {25, 88}, {27, 90}, {29, 92},
{31, 94}, {33, 96}, {35, 98}, {37, 100}, {39, 102}, {41, 104}, {43, 106}, {45,
108}, {47, 110}, {49, 112}, {128, 194}, {129, 195}, {132, 198}, {133, 199},
{136, 202}, {137, 203}, {140, 206}, {141, 207}, {144, 210}, {145, 211}, {148,
214}, {149, 215}, {152, 218}, {153, 219}, {156, 222}, {157, 223}, {160, 226},
{161, 227}, {164, 230}, {165, 231}, {168, 234}, {169, 235}, {172, 238}, {173,
239}, {176, 242}, {177, 243}, {180, 246}, {181, 247}, {184, 250}, {185, 251},
{188, 254}, {189, 255}, {1, 66}, {62, 125}, {58, 121}, {54, 117}, {50, 113}, {6,
69}, {10, 73}, {14, 77}, {18, 81}, {22, 85}, {26, 89}, {30, 93}, {34, 97}, {38,
101}, {42, 105}, {46, 109}, {130, 196}, {131, 197}, {138, 204}, {139, 205},
{146, 212}, {147, 213}, {154, 220}, {155, 221}, {162, 228}, {163, 229}, {170,
236}, {171, 237}, {178, 244}, {179, 245}, {186, 252}, {187, 253}, {4, 67}, {60,
123}, {52, 115}, {12, 75}, {20, 83}, {28, 91}, {36, 99}, {44, 107}, {134, 200},
{135, 201}, {150, 216}, {151, 217}, {166, 232}, {167, 233}, {182, 248}, {183,
249}, {8, 71}, {56, 119}, {24, 87}, {40, 103}, {128, 219}, {132, 223}, {129,
220}, {131, 222}, {142, 208}, {143, 209}, {174, 240}, {175, 241}, {16, 79}, {48,
111}, {130, 221}, {158, 224}, {159, 225}, {32, 95}, {63, 64}, {2, 131}, {1,
130}, {1, 133}, {66, 198}, {65, 197}, {64, 196}, {59, 191}, {58, 190}, {57,
189}, {56, 188}, {51, 183}, {50, 182}, {2, 134}, {3, 135}, {8, 140}, {9, 141},
{10, 142}, {11, 143}, {16, 148}, {17, 149}, {18, 150}, {19, 151}, {24, 156},
{25, 157}, {26, 158}, {27, 159}, {32, 164}, {33, 165}, {34, 166}, {35, 167},
{40, 172}, {41, 173}, {42, 174}, {43, 175}, {48, 180}, {49, 181}, {3, 132}, {4,
136}, {55, 187}, {54, 186}, {53, 185}, {52, 184}, {5, 137}, {6, 138}, {7, 139},
{20, 152}, {21, 153}, {22, 154}, {23, 155}, {36, 168}, {37, 169}, {38, 170},
{39, 171}, {12, 144}, {13, 145}, {14, 146}, {15, 147}, {44, 176}, {45, 177},
{46, 178}, {47, 179}, {96, 253}, {98, 255}, {97, 254}, {67, 224}, {87, 244},
{83, 240}, {79, 236}, {75, 232}, {71, 228}, {91, 248}, {95, 252}, {68, 225},
{86, 243}, {84, 241}, {78, 235}, {76, 233}, {70, 227}, {92, 249}, {94, 251},
{109, 200}, {111, 202}, {117, 208}, {119, 210}, {125, 216}, {127, 218}, {69,
226}, {85, 242}, {77, 234}, {93, 250}, {110, 201}, {118, 209}, {126, 217}, {104,
192}, {105, 193}, {106, 194}, {107, 195}, {108, 196}, {109, 197}, {110, 198},
{108, 199}, {120, 211}, {124, 215}, {72, 229}, {88, 245}, {74, 231}, {90, 247},
{121, 212}, {123, 214}, {73, 230}, {89, 246}, {122, 213}, {112, 203}, {116,
207}, {28, 160}, {29, 161}, {30, 162}, {31, 163}, {80, 237}, {82, 239}, {113,
204}, {115, 206}, {126, 192}, {127, 193}, {81, 238}, {114, 205}, {65, 128}, {68,
134}, {89, 155}, {88, 154}, {85, 151}, {84, 150}, {81, 147}, {80, 146}, {77,
143}, {76, 142}, {73, 139}, {72, 138}, {69, 135}, {92, 158}, {93, 159}, {96,
162}, {97, 163}, {100, 166}, {101, 167}, {104, 170}, {105, 171}, {108, 174},
{109, 175}, {112, 178}, {113, 179}, {116, 182}, {117, 183}, {120, 186}, {121,
187}, {124, 190}, {125, 191}, {66, 129}, {67, 133}, {83, 149}, {82, 148}, {75,
141}, {74, 140}, {90, 156}, {91, 157}, {98, 164}, {99, 165}, {106, 172}, {107,
173}, {114, 180}, {115, 181}, {122, 188}, {123, 189}, {70, 136}, {87, 153}, {86,
152}, {71, 137}, {102, 168}, {103, 169}, {118, 184}, {119, 185}, {67, 155}, {71,
159}, {70, 158}, {69, 157}, {68, 156}, {96, 184}, {97, 185}, {98, 186}, {99,
187}, {100, 188}, {101, 189}, {102, 190}, {103, 191}, {78, 144}, {79, 145},
{110, 176}, {111, 177}, {72, 160}, {89, 177}, {88, 176}, {79, 167}, {78, 166},
{77, 165}, {76, 164}, {75, 163}, {74, 162}, {73, 161}, {90, 178}, {91, 179},
{92, 180}, {93, 181}, {94, 182}, {95, 183}, {111, 133}, {122, 144}, {123, 145},
{126, 148}, {127, 149}, {124, 146}, {125, 147}, {112, 134}, {113, 135}, {120,
142}, {121, 143}, {80, 168}, {87, 175}, {86, 174}, {85, 173}, {84, 172}, {83,
171}, {82, 170}, {81, 169}, {114, 136}, {115, 137}, {118, 140}, {119, 141}, {60,
192}, {63, 195}, {62, 194}, {61, 193}, {94, 160}, {95, 161}, {116, 138}, {117,
139}, {99, 256}, {103, 260}, {107, 264}, {100, 257}, {102, 259}, {101, 258},
{104, 261}, {106, 263}, {105, 262}, {190, 256}, {191, 257}, {192, 258}, {193,
259}, {196, 262}, {197, 263}, {194, 260}, {195, 261}, {198, 264}, {213, 256},
{221, 264}, {215, 258}, {214, 257}, {216, 259}, {220, 263}, {217, 260}, {219,
262}, {218, 261}, {233, 256}, {239, 262}, {237, 260}, {235, 258}, {234, 257},
{238, 261}, {236, 259}, {240, 263}, {241, 264} }>;
(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, 130)(3, 196)(4, 64)(5, 127)(6, 193)(7, 61)(8, 124)(9, 190)(10, 58)(11,
121)(12, 187)(13, 55)(14, 118)(15, 184)(16, 52)(17, 115)(18, 181)(19, 49)(20,
112)(21, 178)(22, 46)(23, 109)(24, 175)(25, 43)(26, 106)(27, 172)(28, 40)(29,
103)(30, 169)(31, 37)(32, 100)(33, 166)(35, 97)(36, 163)(38, 94)(39, 160)(41,
91)(42, 157)(44, 88)(45, 154)(47, 85)(48, 151)(50, 82)(51, 148)(53, 79)(54,
145)(56, 76)(57, 142)(59, 73)(60, 139)(62, 70)(63, 136)(65, 67)(66, 133)(68,
218)(69, 105)(71, 215)(72, 102)(74, 212)(75, 99)(77, 209)(78, 96)(80, 206)(81,
93)(83, 203)(84, 90)(86, 200)(89, 263)(92, 260)(95, 257)(98, 254)(101, 251)(104,
248)(107, 245)(108, 132)(110, 242)(111, 129)(113, 239)(114, 126)(116, 236)(117,
123)(119, 233)(122, 230)(125, 227)(128, 224)(131, 221)(134, 152)(135, 262)(137,
149)(138, 259)(140, 146)(141, 256)(144, 253)(147, 250)(150, 247)(153, 244)(155,
197)(156, 241)(158, 194)(159, 238)(161, 191)(162, 235)(164, 188)(165, 232)(167,
185)(168, 229)(170, 182)(171, 226)(173, 179)(174, 223)(177, 220)(180, 217)(183,
214)(186, 211)(189, 208)(192, 205)(195, 202)(198, 199)(201, 219)(204, 216)(207,
213)(222, 264)(225, 261)(228, 258)(231, 255)(234, 252)(237, 249)(240, 246) (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, 66)(3, 65)(4, 64)(5, 63)(6, 62)(7, 61)(8, 60)(9, 59)(10, 58)(11, 57)(12,
56)(13, 55)(14, 54)(15, 53)(16, 52)(17, 51)(18, 50)(19, 49)(20, 48)(21, 47)(22,
46)(23, 45)(24, 44)(25, 43)(26, 42)(27, 41)(28, 40)(29, 39)(30, 38)(31, 37)(32,
36)(33, 35)(67, 196)(68, 195)(69, 194)(70, 193)(71, 192)(72, 191)(73, 190)(74,
189)(75, 188)(76, 187)(77, 186)(78, 185)(79, 184)(80, 183)(81, 182)(82, 181)(83,
180)(84, 179)(85, 178)(86, 177)(87, 176)(88, 175)(89, 174)(90, 173)(91, 172)(92,
171)(93, 170)(94, 169)(95, 168)(96, 167)(97, 166)(98, 165)(99, 164)(100,
163)(101, 162)(102, 161)(103, 160)(104, 159)(105, 158)(106, 157)(107, 156)(108,
155)(109, 154)(110, 153)(111, 152)(112, 151)(113, 150)(114, 149)(115, 148)(116,
147)(117, 146)(118, 145)(119, 144)(120, 143)(121, 142)(122, 141)(123, 140)(124,
139)(125, 138)(126, 137)(127, 136)(128, 135)(129, 134)(130, 133)(131, 198)(132,
197)(199, 221)(200, 220)(201, 219)(202, 218)(203, 217)(204, 216)(205, 215)(206,
214)(207, 213)(208, 212)(209, 211)(222, 264)(223, 263)(224, 262)(225, 261)(226,
260)(227, 259)(228, 258)(229, 257)(230, 256)(231, 255)(232, 254)(233, 253)(234,
252)(235, 251)(236, 250)(237, 249)(238, 248)(239, 247)(240, 246)(241, 245)(242,
244)
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)
C4[ 264, 20 ]
264
-1 66 133 2 130
-2 1 134 3 131
-3 132 2 135 4
-4 67 3 136 5
-5 68 4 137 6
-6 69 5 138 7
-7 70 6 139 8
-8 71 7 140 9
-9 72 8 141 10
-10 11 73 9 142
-11 143 12 74 10
-12 11 144 13 75
-13 12 145 14 76
-14 77 13 146 15
-15 78 14 147 16
-16 79 15 148 17
-17 80 16 149 18
-18 81 17 150 19
-19 82 18 151 20
-20 83 19 152 21
-21 22 84 20 153
-22 154 23 85 21
-23 22 155 24 86
-24 23 156 25 87
-25 88 24 157 26
-26 89 25 158 27
-27 90 26 159 28
-28 91 27 160 29
-29 92 28 161 30
-30 93 29 162 31
-31 94 30 163 32
-32 33 95 31 164
-33 165 34 96 32
-34 33 166 35 97
-35 34 167 36 98
-36 99 35 168 37
-37 100 36 169 38
-38 101 37 170 39
-39 102 38 171 40
-40 103 39 172 41
-41 104 40 173 42
-42 105 41 174 43
-43 44 106 42 175
-44 176 45 107 43
-45 44 177 46 108
-46 45 178 47 109
-47 110 46 179 48
-48 111 47 180 49
-49 112 48 181 50
-50 113 49 182 51
-51 114 50 183 52
-52 115 51 184 53
-53 116 52 185 54
-54 55 117 53 186
-55 187 56 118 54
-56 55 188 57 119
-57 56 189 58 120
-58 121 57 190 59
-59 122 58 191 60
-60 123 59 192 61
-61 124 60 193 62
-62 125 61 194 63
-63 126 62 195 64
-64 127 63 196 65
-65 66 128 64 197
-66 198 1 129 65
-67 133 155 4 224
-68 134 156 5 225
-69 135 157 6 226
-70 136 158 7 227
-71 137 159 8 228
-72 138 160 9 229
-73 139 161 10 230
-74 11 231 140 162
-75 12 232 141 163
-76 13 233 142 164
-77 143 165 14 234
-78 144 166 15 235
-79 145 167 16 236
-80 146 168 17 237
-81 147 169 18 238
-82 148 170 19 239
-83 149 171 20 240
-84 150 172 21 241
-85 22 242 151 173
-86 23 243 152 174
-87 24 244 153 175
-88 154 176 25 245
-89 155 177 26 246
-90 156 178 27 247
-91 157 179 28 248
-92 158 180 29 249
-93 159 181 30 250
-94 160 182 31 251
-95 161 183 32 252
-96 33 253 162 184
-97 34 254 163 185
-98 35 255 164 186
-99 165 187 36 256
-100 166 188 37 257
-101 167 189 38 258
-102 168 190 39 259
-103 169 191 40 260
-104 170 192 41 261
-105 171 193 42 262
-106 172 194 43 263
-107 44 264 173 195
-108 45 199 174 196
-109 46 200 175 197
-110 176 198 47 201
-111 133 177 48 202
-112 134 178 49 203
-113 135 179 50 204
-114 136 180 51 205
-115 137 181 52 206
-116 138 182 53 207
-117 139 183 54 208
-118 55 209 140 184
-119 56 210 141 185
-120 57 211 142 186
-121 143 187 58 212
-122 144 188 59 213
-123 145 189 60 214
-124 146 190 61 215
-125 147 191 62 216
-126 148 192 63 217
-127 149 193 64 218
-128 150 194 65 219
-129 66 220 151 195
-130 1 221 152 196
-131 2 222 153 197
-132 154 198 3 223
-133 1 111 199 67
-134 68 2 112 200
-135 69 3 113 201
-136 70 4 114 202
-137 71 5 115 203
-138 204 72 6 116
-139 205 73 7 117
-140 206 74 8 118
-141 119 207 75 9
-142 120 208 76 10
-143 121 209 77 11
-144 122 210 78 12
-145 123 211 79 13
-146 124 212 80 14
-147 125 213 81 15
-148 126 214 82 16
-149 17 127 215 83
-150 18 128 216 84
-151 85 19 129 217
-152 86 20 130 218
-153 87 21 131 219
-154 88 22 132 220
-155 221 89 23 67
-156 68 222 90 24
-157 69 223 91 25
-158 70 224 92 26
-159 71 225 93 27
-160 72 226 94 28
-161 73 227 95 29
-162 74 228 96 30
-163 75 229 97 31
-164 76 230 98 32
-165 77 231 99 33
-166 34 78 232 100
-167 35 79 233 101
-168 102 36 80 234
-169 103 37 81 235
-170 104 38 82 236
-171 105 39 83 237
-172 238 106 40 84
-173 85 239 107 41
-174 86 240 108 42
-175 87 241 109 43
-176 88 242 110 44
-177 89 243 111 45
-178 90 244 112 46
-179 91 245 113 47
-180 92 246 114 48
-181 93 247 115 49
-182 94 248 116 50
-183 51 95 249 117
-184 52 96 250 118
-185 119 53 97 251
-186 120 54 98 252
-187 121 55 99 253
-188 122 56 100 254
-189 255 123 57 101
-190 102 256 124 58
-191 103 257 125 59
-192 104 258 126 60
-193 105 259 127 61
-194 106 260 128 62
-195 107 261 129 63
-196 108 262 130 64
-197 109 263 131 65
-198 110 264 132 66
-199 242 133 222 108
-200 243 134 223 109
-201 110 244 135 224
-202 111 245 136 225
-203 112 246 137 226
-204 113 247 138 227
-205 114 248 139 228
-206 115 249 140 229
-207 116 250 141 230
-208 231 117 251 142
-209 143 232 118 252
-210 253 144 233 119
-211 254 145 234 120
-212 121 255 146 235
-213 122 256 147 236
-214 123 257 148 237
-215 124 258 149 238
-216 125 259 150 239
-217 126 260 151 240
-218 127 261 152 241
-219 242 128 262 153
-220 154 243 129 263
-221 264 155 244 130
-222 199 156 245 131
-223 132 200 157 246
-224 67 201 158 247
-225 68 202 159 248
-226 69 203 160 249
-227 70 204 161 250
-228 71 205 162 251
-229 72 206 163 252
-230 253 73 207 164
-231 165 254 74 208
-232 209 166 255 75
-233 210 167 256 76
-234 77 211 168 257
-235 78 212 169 258
-236 79 213 170 259
-237 80 214 171 260
-238 81 215 172 261
-239 82 216 173 262
-240 83 217 174 263
-241 264 84 218 175
-242 176 199 85 219
-243 220 177 200 86
-244 221 178 201 87
-245 88 222 179 202
-246 89 223 180 203
-247 90 224 181 204
-248 91 225 182 205
-249 92 226 183 206
-250 93 227 184 207
-251 94 228 185 208
-252 209 95 229 186
-253 187 210 96 230
-254 231 188 211 97
-255 232 189 212 98
-256 99 233 190 213
-257 100 234 191 214
-258 101 235 192 215
-259 102 236 193 216
-260 103 237 194 217
-261 104 238 195 218
-262 105 239 196 219
-263 220 106 240 197
-264 198 221 107 241
0