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