Graph forms
for C4 [ 243, 12 ] = AMC(3,9,[1.8:3.7])
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On this page are computer-accessible forms for the graph C4[ 243, 12 ] =
AMC(3,9,[1.8:3.7]).
(I) Following is a form readable by MAGMA:
g:=Graph<243|{ {160, 168}, {162, 170}, {161, 169}, {80, 89}, {81, 90}, {79, 88},
{74, 83}, {76, 85}, {78, 87}, {73, 82}, {77, 86}, {75, 84}, {154, 171}, {155,
163}, {159, 167}, {158, 166}, {157, 165}, {156, 164}, {135, 199}, {162, 226},
{153, 217}, {144, 208}, {16, 88}, {55, 127}, {54, 126}, {53, 125}, {52, 124},
{51, 123}, {50, 122}, {49, 121}, {48, 120}, {39, 111}, {38, 110}, {17, 89}, {18,
90}, {19, 91}, {20, 92}, {21, 93}, {22, 94}, {23, 95}, {32, 104}, {33, 105},
{34, 106}, {35, 107}, {36, 108}, {37, 109}, {128, 201}, {160, 233}, {150, 223},
{148, 221}, {146, 219}, {134, 207}, {132, 205}, {130, 203}, {129, 202}, {161,
234}, {149, 222}, {145, 218}, {133, 206}, {131, 204}, {147, 220}, {143, 216},
{10, 82}, {47, 119}, {46, 118}, {45, 117}, {44, 116}, {43, 115}, {42, 114}, {41,
113}, {40, 112}, {11, 83}, {12, 84}, {13, 85}, {14, 86}, {15, 87}, {128, 217},
{142, 215}, {140, 213}, {138, 211}, {136, 209}, {134, 223}, {132, 221}, {130,
219}, {1, 91}, {4, 94}, {5, 95}, {32, 122}, {33, 123}, {36, 126}, {37, 127},
{129, 218}, {141, 214}, {137, 210}, {133, 222}, {2, 92}, {3, 93}, {34, 124},
{35, 125}, {131, 220}, {139, 212}, {136, 234}, {145, 243}, {6, 96}, {7, 97},
{14, 104}, {15, 105}, {22, 112}, {23, 113}, {30, 120}, {31, 121}, {135, 224},
{151, 240}, {143, 232}, {138, 227}, {152, 241}, {142, 231}, {140, 229}, {8, 98},
{9, 99}, {12, 102}, {13, 103}, {24, 114}, {25, 115}, {28, 118}, {29, 119}, {137,
226}, {153, 242}, {141, 230}, {10, 100}, {11, 101}, {26, 116}, {27, 117}, {139,
228}, {151, 224}, {159, 232}, {24, 96}, {25, 97}, {26, 98}, {27, 99}, {28, 100},
{29, 101}, {30, 102}, {31, 103}, {144, 233}, {158, 231}, {156, 229}, {154, 227},
{152, 225}, {150, 239}, {148, 237}, {146, 235}, {16, 106}, {17, 107}, {20, 110},
{21, 111}, {149, 238}, {157, 230}, {18, 108}, {19, 109}, {147, 236}, {155, 228},
{36, 172}, {54, 190}, {81, 217}, {32, 177}, {46, 191}, {44, 189}, {42, 187},
{40, 185}, {38, 183}, {34, 179}, {64, 209}, {66, 211}, {68, 213}, {70, 215},
{74, 219}, {76, 221}, {78, 223}, {33, 178}, {41, 186}, {37, 182}, {65, 210},
{69, 214}, {73, 218}, {77, 222}, {35, 180}, {43, 188}, {67, 212}, {75, 220},
{45, 181}, {72, 208}, {2, 155}, {4, 157}, {6, 159}, {1, 154}, {5, 158}, {127,
225}, {3, 156}, {39, 184}, {71, 216}, {100, 198}, {109, 207}, {38, 128}, {55,
145}, {54, 144}, {47, 137}, {46, 136}, {39, 129}, {62, 152}, {63, 153}, {86,
240}, {87, 241}, {7, 160}, {119, 208}, {103, 192}, {111, 200}, {8, 161}, {126,
215}, {124, 213}, {122, 211}, {120, 209}, {104, 193}, {106, 195}, {108, 197},
{110, 199}, {40, 130}, {57, 147}, {56, 146}, {45, 135}, {44, 134}, {41, 131},
{60, 150}, {61, 151}, {88, 242}, {89, 243}, {9, 162}, {125, 214}, {121, 210},
{105, 194}, {42, 132}, {118, 216}, {58, 148}, {43, 133}, {59, 149}, {31, 176},
{123, 212}, {79, 224}, {107, 196}, {20, 165}, {22, 167}, {24, 169}, {26, 171},
{28, 173}, {30, 175}, {80, 225}, {90, 235}, {4, 183}, {8, 187}, {12, 191}, {21,
166}, {25, 170}, {29, 174}, {3, 182}, {9, 188}, {11, 190}, {2, 181}, {127, 200},
{119, 192}, {19, 164}, {27, 163}, {59, 131}, {58, 130}, {57, 129}, {56, 128},
{60, 132}, {61, 133}, {62, 134}, {63, 135}, {112, 201}, {124, 197}, {122, 195},
{120, 193}, {116, 205}, {114, 203}, {48, 138}, {53, 143}, {52, 142}, {49, 139},
{84, 238}, {85, 239}, {113, 202}, {125, 198}, {121, 194}, {117, 206}, {1, 189},
{5, 184}, {7, 186}, {50, 140}, {51, 141}, {82, 236}, {83, 237}, {6, 185}, {123,
196}, {115, 204}, {23, 168}, {99, 163}, {126, 190}, {117, 181}, {108, 172}, {28,
216}, {55, 243}, {46, 234}, {37, 225}, {64, 136}, {65, 137}, {66, 138}, {67,
139}, {68, 140}, {69, 141}, {70, 142}, {71, 143}, {80, 152}, {81, 153}, {96,
169}, {118, 191}, {116, 189}, {98, 171}, {100, 173}, {102, 175}, {112, 185},
{114, 187}, {97, 170}, {101, 174}, {113, 186}, {10, 198}, {13, 192}, {47, 226},
{45, 224}, {15, 194}, {29, 208}, {31, 210}, {61, 240}, {63, 242}, {14, 193},
{115, 188}, {30, 209}, {62, 241}, {16, 195}, {56, 235}, {52, 231}, {48, 227},
{20, 199}, {24, 203}, {60, 239}, {17, 196}, {57, 236}, {51, 230}, {49, 228},
{25, 204}, {27, 206}, {59, 238}, {18, 197}, {58, 237}, {50, 229}, {26, 205},
{103, 176}, {111, 184}, {72, 144}, {73, 145}, {74, 146}, {75, 147}, {76, 148},
{77, 149}, {78, 150}, {79, 151}, {96, 185}, {98, 187}, {102, 191}, {104, 177},
{106, 179}, {110, 183}, {64, 154}, {65, 155}, {68, 158}, {69, 159}, {97, 186},
{101, 190}, {105, 178}, {109, 182}, {19, 207}, {21, 200}, {53, 232}, {23, 202},
{66, 156}, {67, 157}, {22, 201}, {54, 233}, {99, 188}, {107, 180}, {1, 227}, {4,
230}, {5, 231}, {8, 234}, {12, 238}, {13, 239}, {16, 242}, {17, 243}, {65, 163},
{68, 166}, {69, 167}, {72, 170}, {76, 174}, {77, 175}, {80, 178}, {81, 179}, {2,
228}, {3, 229}, {10, 236}, {11, 237}, {66, 164}, {67, 165}, {70, 160}, {71,
161}, {74, 172}, {75, 173}, {82, 180}, {91, 189}, {87, 176}, {95, 184}, {88,
177}, {90, 179}, {92, 181}, {94, 183}, {72, 162}, {9, 226}, {64, 171}, {89,
178}, {93, 182}, {6, 232}, {7, 233}, {70, 168}, {71, 169}, {47, 192}, {48, 193},
{58, 203}, {56, 201}, {52, 197}, {50, 195}, {60, 205}, {62, 207}, {32, 211},
{57, 202}, {53, 198}, {49, 194}, {44, 223}, {40, 219}, {36, 215}, {61, 206},
{33, 212}, {43, 222}, {41, 220}, {35, 214}, {34, 213}, {51, 196}, {42, 221},
{59, 204}, {95, 168}, {63, 199}, {18, 235}, {84, 173}, {86, 175}, {92, 165},
{94, 167}, {85, 174}, {93, 166}, {39, 218}, {73, 180}, {14, 240}, {15, 241},
{78, 176}, {79, 177}, {38, 217}, {55, 200}, {83, 172}, {91, 164} }>;
(II) A more general form is to represent the graph as the orbit of {160, 168}
under the group generated by the following permutations:
a: (1, 10, 19, 28, 37, 46, 55, 64, 73)(2, 11, 20, 29, 38, 47, 56, 65, 74)(3, 12,
21, 30, 39, 48, 57, 66, 75)(4, 13, 22, 31, 40, 49, 58, 67, 76)(5, 14, 23, 32,
41, 50, 59, 68, 77)(6, 15, 24, 33, 42, 51, 60, 69, 78)(7, 16, 25, 34, 43, 52,
61, 70, 79)(8, 17, 26, 35, 44, 53, 62, 71, 80)(9, 18, 27, 36, 45, 54, 63, 72,
81)(82, 91, 100, 109, 118, 127, 136, 145, 154)(83, 92, 101, 110, 119, 128, 137,
146, 155)(84, 93, 102, 111, 120, 129, 138, 147, 156)(85, 94, 103, 112, 121, 130,
139, 148, 157)(86, 95, 104, 113, 122, 131, 140, 149, 158)(87, 96, 105, 114, 123,
132, 141, 150, 159)(88, 97, 106, 115, 124, 133, 142, 151, 160)(89, 98, 107, 116,
125, 134, 143, 152, 161)(90, 99, 108, 117, 126, 135, 144, 153, 162)(163, 172,
181, 190, 199, 208, 217, 226, 235)(164, 173, 182, 191, 200, 209, 218, 227,
236)(165, 174, 183, 192, 201, 210, 219, 228, 237)(166, 175, 184, 193, 202, 211,
220, 229, 238)(167, 176, 185, 194, 203, 212, 221, 230, 239)(168, 177, 186, 195,
204, 213, 222, 231, 240)(169, 178, 187, 196, 205, 214, 223, 232, 241)(170, 179,
188, 197, 206, 215, 224, 233, 242)(171, 180, 189, 198, 207, 216, 225, 234,
243) (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, 35)(3, 60)(5, 29)(6, 63)(8, 32)(9, 57)(10, 27)(11, 52)(12, 77)(13,
21)(14, 46)(15, 80)(16, 24)(17, 49)(18, 74)(19, 44)(20, 69)(22, 38)(23, 72)(25,
41)(26, 66)(28, 61)(31, 55)(34, 58)(37, 78)(39, 47)(40, 81)(42, 50)(43, 75)(45,
53)(48, 64)(51, 67)(54, 70)(65, 73)(68, 76)(71, 79)(82, 163)(83, 197)(84,
222)(85, 166)(86, 191)(87, 225)(88, 169)(89, 194)(90, 219)(91, 189)(92, 214)(93,
239)(94, 183)(95, 208)(96, 242)(97, 186)(98, 211)(99, 236)(100, 206)(101,
231)(102, 175)(103, 200)(104, 234)(105, 178)(106, 203)(107, 228)(108, 172)(109,
223)(110, 167)(111, 192)(112, 217)(113, 170)(114, 195)(115, 220)(116, 164)(117,
198)(118, 240)(119, 184)(120, 209)(121, 243)(122, 187)(123, 212)(124, 237)(125,
181)(126, 215)(127, 176)(128, 201)(129, 226)(130, 179)(131, 204)(132, 229)(133,
173)(134, 207)(135, 232)(136, 193)(137, 218)(138, 171)(139, 196)(140, 221)(141,
165)(142, 190)(143, 224)(144, 168)(145, 210)(146, 235)(147, 188)(148, 213)(149,
238)(150, 182)(151, 216)(152, 241)(153, 185)(154, 227)(155, 180)(156, 205)(157,
230)(158, 174)(159, 199)(160, 233)(161, 177)(162, 202)
c: (2, 57)(3, 32)(4, 7)(5, 63)(6, 29)(8, 60)(9, 35)(10, 65)(11, 40)(12, 15)(13,
71)(14, 37)(16, 68)(17, 43)(19, 48)(20, 23)(21, 79)(22, 54)(24, 76)(25, 51)(27,
73)(28, 31)(30, 62)(33, 59)(36, 56)(38, 70)(39, 45)(41, 67)(44, 64)(46, 78)(47,
53)(49, 75)(52, 81)(55, 61)(69, 72)(77, 80)(82, 163)(83, 219)(84, 194)(85,
169)(86, 225)(87, 191)(88, 166)(89, 222)(90, 197)(91, 227)(92, 202)(93, 177)(94,
233)(95, 199)(96, 174)(97, 230)(98, 205)(99, 180)(100, 210)(101, 185)(102,
241)(103, 216)(104, 182)(105, 238)(106, 213)(107, 188)(108, 235)(109, 193)(110,
168)(111, 224)(112, 190)(113, 165)(114, 221)(115, 196)(116, 171)(117, 218)(118,
176)(119, 232)(120, 207)(121, 173)(122, 229)(123, 204)(124, 179)(125, 226)(126,
201)(127, 240)(128, 215)(129, 181)(130, 237)(131, 212)(132, 187)(133, 243)(134,
209)(135, 184)(136, 223)(137, 198)(138, 164)(139, 220)(140, 195)(141, 170)(142,
217)(143, 192)(144, 167)(145, 206)(146, 172)(147, 228)(148, 203)(149, 178)(150,
234)(151, 200)(152, 175)(153, 231)(154, 189)(155, 236)(156, 211)(157, 186)(158,
242)(159, 208)(160, 183)(161, 239)(162, 214)
d: (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)
e: (1, 82, 163)(2, 116, 218)(3, 141, 192)(4, 85, 166)(5, 110, 221)(6, 144,
195)(7, 88, 169)(8, 113, 224)(9, 138, 198)(10, 99, 227)(11, 124, 201)(12, 149,
175)(13, 93, 230)(14, 118, 204)(15, 152, 178)(16, 96, 233)(17, 121, 207)(18,
146, 172)(19, 107, 210)(20, 132, 184)(21, 157, 239)(22, 101, 213)(23, 135,
187)(24, 160, 242)(25, 104, 216)(26, 129, 181)(27, 154, 236)(28, 115, 193)(29,
140, 167)(30, 84, 222)(31, 109, 196)(32, 143, 170)(33, 87, 225)(34, 112,
190)(35, 137, 164)(36, 90, 219)(37, 123, 176)(38, 148, 231)(39, 92, 205)(40,
126, 179)(41, 151, 234)(42, 95, 199)(43, 120, 173)(44, 145, 228)(45, 98,
202)(46, 131, 240)(47, 156, 214)(48, 100, 188)(49, 134, 243)(50, 159, 208)(51,
103, 182)(52, 128, 237)(53, 162, 211)(54, 106, 185)(55, 139, 223)(56, 83,
197)(57, 117, 171)(58, 142, 217)(59, 86, 191)(60, 111, 165)(61, 136, 220)(62,
89, 194)(63, 114, 168)(64, 147, 206)(65, 91, 180)(66, 125, 226)(67, 150,
200)(68, 94, 174)(69, 119, 229)(70, 153, 203)(71, 97, 177)(72, 122, 232)(73,
155, 189)(74, 108, 235)(75, 133, 209)(76, 158, 183)(77, 102, 238)(78, 127,
212)(79, 161, 186)(80, 105, 241)(81, 130, 215)
C4[ 243, 12 ]
243
-1 154 189 91 227
-2 155 92 181 228
-3 156 93 182 229
-4 157 94 183 230
-5 231 158 95 184
-6 232 159 96 185
-7 233 160 97 186
-8 187 234 161 98
-9 99 188 226 162
-10 198 100 82 236
-11 101 190 83 237
-12 102 191 84 238
-13 103 192 85 239
-14 104 193 86 240
-15 105 194 87 241
-16 88 242 106 195
-17 89 243 107 196
-18 90 235 108 197
-19 91 207 109 164
-20 110 165 199 92
-21 111 166 200 93
-22 112 167 201 94
-23 113 168 202 95
-24 114 169 203 96
-25 115 170 204 97
-26 116 171 205 98
-27 99 117 206 163
-28 100 216 118 173
-29 101 119 174 208
-30 209 102 120 175
-31 121 176 210 103
-32 122 177 211 104
-33 123 178 212 105
-34 124 179 213 106
-35 125 180 214 107
-36 126 215 172 108
-37 225 127 182 109
-38 110 128 183 217
-39 111 129 184 218
-40 112 130 185 219
-41 220 113 131 186
-42 132 187 221 114
-43 133 188 222 115
-44 134 189 223 116
-45 135 224 181 117
-46 234 136 191 118
-47 137 192 226 119
-48 138 193 227 120
-49 121 139 194 228
-50 122 140 195 229
-51 123 141 196 230
-52 231 124 142 197
-53 143 198 232 125
-54 144 233 190 126
-55 243 145 200 127
-56 146 201 235 128
-57 147 202 236 129
-58 148 203 237 130
-59 149 204 238 131
-60 132 150 205 239
-61 133 151 206 240
-62 134 152 207 241
-63 242 199 135 153
-64 154 209 136 171
-65 155 210 137 163
-66 156 211 138 164
-67 165 157 212 139
-68 166 158 213 140
-69 167 159 214 141
-70 168 160 215 142
-71 143 169 161 216
-72 144 170 162 208
-73 145 180 82 218
-74 146 83 172 219
-75 220 147 84 173
-76 221 148 85 174
-77 222 149 86 175
-78 176 223 150 87
-79 88 177 224 151
-80 89 178 225 152
-81 90 179 217 153
-82 180 236 73 10
-83 11 237 172 74
-84 12 238 173 75
-85 13 239 174 76
-86 77 14 240 175
-87 176 78 15 241
-88 242 177 79 16
-89 243 178 80 17
-90 179 81 235 18
-91 1 189 19 164
-92 165 2 181 20
-93 166 3 182 21
-94 22 167 4 183
-95 23 168 5 184
-96 24 169 6 185
-97 25 170 7 186
-98 187 26 171 8
-99 188 27 9 163
-100 198 28 173 10
-101 11 190 29 174
-102 12 191 30 175
-103 176 13 192 31
-104 177 14 193 32
-105 33 178 15 194
-106 34 179 16 195
-107 35 180 17 196
-108 36 18 172 197
-109 37 182 19 207
-110 199 38 183 20
-111 200 39 184 21
-112 22 201 40 185
-113 23 202 41 186
-114 187 24 203 42
-115 188 25 204 43
-116 44 189 26 205
-117 45 27 181 206
-118 46 191 28 216
-119 47 192 29 208
-120 209 48 193 30
-121 210 49 194 31
-122 211 50 195 32
-123 33 212 51 196
-124 34 213 52 197
-125 198 35 214 53
-126 36 190 215 54
-127 55 200 37 225
-128 56 201 38 217
-129 57 202 39 218
-130 58 203 40 219
-131 220 59 204 41
-132 221 60 205 42
-133 222 61 206 43
-134 44 223 62 207
-135 45 199 224 63
-136 209 46 234 64
-137 210 47 226 65
-138 66 211 48 227
-139 67 212 49 228
-140 68 213 50 229
-141 69 214 51 230
-142 231 70 215 52
-143 232 71 216 53
-144 233 72 54 208
-145 55 243 73 218
-146 56 235 74 219
-147 220 57 236 75
-148 221 58 237 76
-149 77 222 59 238
-150 78 223 60 239
-151 79 224 61 240
-152 80 225 62 241
-153 242 81 63 217
-154 1 171 227 64
-155 2 228 163 65
-156 66 3 229 164
-157 165 67 4 230
-158 231 166 68 5
-159 232 167 69 6
-160 233 168 70 7
-161 234 169 71 8
-162 170 72 226 9
-163 99 155 27 65
-164 66 156 91 19
-165 67 157 92 20
-166 68 158 93 21
-167 22 69 159 94
-168 23 70 160 95
-169 24 71 161 96
-170 25 72 162 97
-171 154 26 64 98
-172 36 83 74 108
-173 100 28 84 75
-174 101 29 85 76
-175 77 102 30 86
-176 78 103 31 87
-177 88 79 104 32
-178 33 89 80 105
-179 34 90 81 106
-180 35 82 73 107
-181 45 2 92 117
-182 3 37 93 109
-183 110 4 38 94
-184 111 5 39 95
-185 112 6 40 96
-186 113 7 41 97
-187 114 8 42 98
-188 99 115 9 43
-189 44 1 91 116
-190 11 101 126 54
-191 12 46 102 118
-192 13 47 103 119
-193 14 48 104 120
-194 121 15 49 105
-195 122 16 50 106
-196 123 17 51 107
-197 124 18 52 108
-198 100 125 53 10
-199 110 135 63 20
-200 55 111 127 21
-201 22 56 112 128
-202 23 57 113 129
-203 24 58 114 130
-204 25 59 115 131
-205 132 26 60 116
-206 133 27 61 117
-207 134 62 19 109
-208 144 72 29 119
-209 136 30 64 120
-210 121 137 31 65
-211 66 122 138 32
-212 33 67 123 139
-213 34 68 124 140
-214 35 69 125 141
-215 36 70 126 142
-216 143 71 28 118
-217 81 38 128 153
-218 145 39 73 129
-219 146 40 74 130
-220 147 41 75 131
-221 132 148 42 76
-222 77 133 149 43
-223 44 78 134 150
-224 45 79 135 151
-225 80 37 127 152
-226 47 137 162 9
-227 154 1 48 138
-228 155 2 49 139
-229 156 3 50 140
-230 157 4 51 141
-231 158 5 52 142
-232 143 159 6 53
-233 144 160 7 54
-234 46 136 161 8
-235 56 90 146 18
-236 57 147 82 10
-237 11 58 148 83
-238 12 59 149 84
-239 13 60 150 85
-240 14 61 151 86
-241 15 62 152 87
-242 88 16 63 153
-243 55 89 145 17
0