Graph forms
for C4 [ 240, 42 ] =
PL(MC3(4,30,1,19,7,10,1),[10^12,12^10])
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On this page are computer-accessible forms for the graph C4[ 240, 42 ] =
PL(MC3(4,30,1,19,7,10,1),[10^12,12^10]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {88, 123}, {88, 125}, {90, 127}, {64, 123}, {67, 127}, {48, 123},
{42, 123}, {41, 124}, {41, 126}, {42, 125}, {39, 122}, {39, 121}, {27, 121},
{30, 124}, {16, 121}, {19, 124}, {11, 122}, {15, 126}, {12, 127}, {15, 124}, {8,
127}, {4, 125}, {2, 126}, {5, 121}, {7, 122}, {3, 125}, {1, 126}, {5, 122}, {69,
197}, {14, 143}, {24, 153}, {28, 157}, {53, 180}, {30, 156}, {78, 205}, {81,
210}, {83, 208}, {99, 224}, {100, 231}, {2, 134}, {58, 190}, {16, 148}, {103,
227}, {10, 143}, {68, 193}, {63, 186}, {80, 213}, {96, 229}, {15, 136}, {62,
185}, {59, 188}, {28, 155}, {9, 129}, {77, 197}, {69, 205}, {14, 134}, {93,
213}, {6, 143}, {33, 168}, {82, 219}, {109, 228}, {110, 231}, {17, 155}, {76,
198}, {23, 157}, {24, 146}, {30, 148}, {107, 225}, {3, 136}, {70, 205}, {13,
129}, {60, 176}, {57, 181}, {32, 173}, {107, 230}, {108, 225}, {42, 164}, {89,
215}, {19, 156}, {35, 179}, {55, 167}, {57, 169}, {26, 139}, {66, 211}, {82,
195}, {35, 177}, {68, 214}, {64, 210}, {57, 171}, {11, 152}, {71, 212}, {43,
184}, {53, 166}, {112, 227}, {113, 226}, {45, 185}, {54, 162}, {85, 193}, {11,
158}, {22, 131}, {20, 130}, {63, 169}, {22, 128}, {47, 185}, {86, 192}, {25,
142}, {26, 141}, {46, 182}, {68, 220}, {51, 171}, {6, 159}, {73, 208}, {53,
172}, {91, 194}, {40, 178}, {120, 226}, {63, 165}, {23, 140}, {36, 191}, {38,
189}, {84, 207}, {10, 150}, {77, 209}, {70, 218}, {29, 128}, {65, 220}, {84,
201}, {8, 150}, {71, 217}, {70, 216}, {37, 187}, {49, 175}, {92, 194}, {7, 152},
{61, 162}, {17, 142}, {32, 191}, {27, 187}, {74, 234}, {2, 163}, {75, 234}, {33,
128}, {98, 195}, {112, 209}, {102, 196}, {3, 160}, {36, 135}, {40, 139}, {48,
147}, {32, 132}, {67, 231}, {62, 154}, {45, 137}, {110, 202}, {99, 198}, {119,
210}, {118, 211}, {115, 214}, {47, 137}, {18, 181}, {37, 141}, {119, 223}, {117,
221}, {54, 158}, {112, 216}, {24, 177}, {58, 147}, {21, 191}, {61, 151}, {29,
183}, {36, 142}, {44, 134}, {46, 132}, {16, 187}, {59, 144}, {8, 164}, {118,
218}, {54, 154}, {105, 197}, {14, 163}, {75, 230}, {79, 226}, {98, 207}, {99,
206}, {103, 202}, {34, 140}, {67, 237}, {15, 160}, {24, 183}, {35, 140}, {101,
202}, {104, 199}, {2, 178}, {44, 156}, {104, 216}, {9, 184}, {12, 189}, {31,
174}, {35, 146}, {109, 220}, {6, 180}, {1, 178}, {91, 239}, {115, 199}, {8,
189}, {115, 198}, {114, 199}, {16, 165}, {85, 224}, {96, 213}, {105, 220}, {110,
219}, {113, 196}, {23, 161}, {52, 130}, {88, 238}, {102, 208}, {103, 209}, {20,
163}, {40, 159}, {83, 228}, {84, 227}, {111, 216}, {21, 173}, {93, 229}, {18,
171}, {60, 133}, {21, 172}, {31, 166}, {50, 139}, {20, 174}, {50, 136}, {46,
149}, {117, 206}, {114, 201}, {86, 237}, {100, 223}, {31, 163}, {42, 150}, {38,
155}, {63, 130}, {55, 138}, {88, 229}, {10, 180}, {116, 202}, {61, 131}, {47,
145}, {99, 221}, {104, 214}, {25, 166}, {97, 222}, {100, 219}, {105, 214}, {31,
223}, {41, 233}, {106, 170}, {22, 215}, {118, 183}, {45, 236}, {84, 149}, {89,
152}, {41, 235}, {120, 186}, {71, 133}, {3, 192}, {12, 207}, {87, 148}, {97,
162}, {112, 179}, {4, 192}, {46, 234}, {52, 240}, {82, 150}, {85, 145}, {101,
161}, {33, 228}, {45, 232}, {25, 223}, {64, 134}, {27, 221}, {40, 238}, {106,
172}, {75, 140}, {90, 157}, {91, 156}, {4, 204}, {73, 129}, {77, 132}, {94,
151}, {39, 236}, {108, 167}, {13, 193}, {27, 215}, {95, 147}, {25, 212}, {117,
184}, {83, 158}, {102, 171}, {14, 192}, {74, 132}, {37, 235}, {81, 159}, {100,
170}, {106, 164}, {111, 161}, {39, 232}, {76, 131}, {96, 175}, {98, 173}, {73,
153}, {116, 164}, {10, 219}, {74, 155}, {26, 203}, {17, 195}, {29, 206}, {66,
145}, {65, 146}, {64, 147}, {81, 130}, {111, 188}, {65, 149}, {78, 154}, {106,
190}, {107, 191}, {76, 153}, {57, 239}, {60, 234}, {9, 222}, {120, 175}, {79,
152}, {48, 231}, {49, 233}, {116, 172}, {72, 144}, {56, 224}, {80, 136}, {86,
142}, {21, 204}, {72, 145}, {86, 143}, {51, 233}, {60, 230}, {59, 225}, {83,
137}, {89, 131}, {96, 186}, {97, 187}, {108, 182}, {114, 168}, {11, 208}, {79,
148}, {43, 240}, {104, 179}, {18, 206}, {87, 139}, {4, 217}, {119, 170}, {77,
144}, {59, 230}, {48, 237}, {23, 201}, {68, 154}, {20, 203}, {28, 195}, {9,
232}, {95, 190}, {56, 218}, {117, 151}, {69, 167}, {101, 135}, {103, 133}, {43,
200}, {62, 221}, {58, 217}, {93, 190}, {80, 180}, {85, 177}, {109, 137}, {13,
232}, {66, 167}, {87, 178}, {111, 138}, {33, 199}, {78, 168}, {94, 184}, {113,
151}, {50, 213}, {102, 129}, {114, 149}, {6, 238}, {119, 159}, {98, 138}, {62,
215}, {110, 135}, {5, 239}, {115, 153}, {38, 204}, {90, 176}, {34, 201}, {81,
186}, {7, 235}, {89, 181}, {107, 135}, {13, 224}, {69, 168}, {1, 239}, {76,
162}, {58, 212}, {7, 233}, {44, 194}, {12, 227}, {101, 138}, {36, 212}, {1,
240}, {116, 133}, {26, 235}, {29, 236}, {32, 209}, {34, 211}, {95, 174}, {108,
157}, {22, 228}, {55, 197}, {87, 165}, {91, 169}, {92, 174}, {49, 194}, {67,
176}, {92, 175}, {66, 182}, {72, 188}, {5, 240}, {120, 141}, {43, 222}, {56,
205}, {19, 229}, {118, 128}, {80, 166}, {51, 196}, {78, 185}, {74, 189}, {71,
176}, {65, 182}, {54, 193}, {93, 170}, {94, 169}, {34, 218}, {75, 179}, {55,
207}, {49, 200}, {72, 177}, {61, 196}, {50, 203}, {53, 204}, {105, 144}, {70,
188}, {79, 181}, {37, 222}, {51, 200}, {90, 161}, {94, 165}, {17, 237}, {30,
226}, {47, 211}, {52, 200}, {92, 160}, {113, 141}, {19, 238}, {28, 225}, {18,
236}, {73, 183}, {44, 210}, {56, 198}, {38, 217}, {52, 203}, {82, 173}, {95,
160}, {97, 158}, {109, 146} }>;
(II) A more general form is to represent the graph as the orbit of {88, 123}
under the group generated by the following permutations:
a: (1, 2)(3, 7)(4, 11)(5, 14)(6, 16)(8, 22)(9, 25)(10, 27)(12, 33)(13, 36)(15,
41)(17, 45)(18, 48)(19, 30)(20, 52)(21, 54)(23, 34)(24, 60)(26, 50)(28, 47)(29,
67)(31, 43)(32, 68)(35, 75)(37, 80)(38, 83)(39, 86)(40, 87)(42, 89)(44, 91)(46,
65)(49, 92)(51, 95)(53, 97)(55, 69)(56, 101)(57, 64)(58, 102)(59, 72)(61,
106)(62, 82)(63, 81)(66, 108)(70, 111)(71, 73)(74, 109)(76, 116)(77, 105)(78,
98)(79, 88)(84, 114)(85, 107)(90, 118)(93, 113)(94, 119)(96, 120)(99, 110)(100,
117)(103, 115)(104, 112)(121, 143)(122, 192)(123, 181)(125, 152)(127, 128)(129,
212)(131, 164)(132, 220)(133, 153)(134, 239)(135, 224)(136, 235)(137, 155)(138,
205)(141, 213)(142, 232)(145, 225)(146, 234)(147, 171)(148, 238)(150, 215)(151,
170)(154, 173)(157, 211)(158, 204)(159, 165)(160, 233)(161, 218)(162, 172)(163,
240)(166, 222)(168, 207)(169, 210)(174, 200)(176, 183)(177, 230)(180, 187)(184,
223)(185, 195)(189, 228)(190, 196)(191, 193)(198, 202)(199, 227)(206, 231)(208,
217)(209, 214)(219, 221)(226, 229)(236, 237) (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: (3, 6)(4, 10)(7, 16)(8, 21)(9, 18)(11, 27)(12, 32)(13, 29)(15, 40)(19,
50)(20, 44)(22, 54)(23, 59)(24, 56)(25, 48)(26, 30)(31, 64)(33, 68)(34, 72)(35,
70)(36, 67)(37, 79)(38, 82)(41, 87)(42, 53)(43, 57)(46, 55)(49, 63)(51, 94)(52,
91)(58, 100)(60, 101)(62, 83)(65, 69)(71, 110)(73, 99)(74, 98)(75, 111)(77,
84)(78, 109)(80, 88)(81, 92)(85, 118)(89, 97)(90, 107)(95, 119)(102, 117)(105,
114)(121, 122)(123, 166)(124, 139)(125, 180)(126, 178)(127, 191)(128, 193)(129,
206)(130, 194)(131, 162)(132, 207)(133, 202)(134, 163)(135, 176)(136, 238)(137,
185)(138, 234)(140, 188)(141, 226)(142, 237)(143, 192)(144, 201)(145, 211)(146,
205)(147, 223)(148, 235)(149, 197)(150, 204)(151, 196)(152, 187)(153, 198)(154,
228)(155, 195)(156, 203)(157, 225)(158, 215)(159, 160)(161, 230)(164, 172)(165,
233)(167, 182)(168, 220)(169, 200)(170, 190)(171, 184)(173, 189)(174, 210)(175,
186)(177, 218)(179, 216)(181, 222)(183, 224)(199, 214)(208, 221)(209, 227)(212,
231)(213, 229)(217, 219)(232, 236)(239, 240)
c: (1, 3, 17, 46, 47, 11)(2, 4, 28, 65, 45, 7)(5, 15, 86, 74, 66, 83)(6, 8, 55,
33, 27, 30)(9, 49, 31, 71, 59, 24)(10, 12, 69, 22, 16, 19)(13, 51, 20, 58, 107,
35)(14, 38, 108, 109, 39, 41)(18, 26, 64, 21, 23, 68)(25, 60, 72, 73, 43,
92)(29, 37, 44, 53, 90, 105)(32, 34, 54, 57, 50, 48)(36, 75, 85, 102, 52,
95)(40, 42, 98, 114, 62, 79)(56, 61, 63, 93, 110, 112)(67, 77, 118, 97, 91,
80)(70, 76, 94, 96, 100, 103)(78, 89, 87, 88, 82, 84)(81, 106, 101, 104, 99,
113)(111, 115, 117, 120, 119, 116)(121, 124, 143, 189, 167, 228)(122, 126, 192,
155, 182, 137)(123, 173, 201, 154, 181, 139)(125, 195, 149, 185, 152, 178)(127,
197, 128, 187, 156, 180)(129, 200, 174, 212, 230, 177)(130, 190, 135, 179, 224,
196)(131, 165, 229, 219, 227, 205)(132, 211, 158, 239, 136, 237)(133, 188, 153,
184, 175, 223)(134, 204, 157, 220, 236, 235)(138, 199, 221, 226, 159, 164)(140,
193, 171, 203, 147, 191)(141, 210, 172, 161, 214, 206)(142, 234, 145, 208, 240,
160)(144, 183, 222, 194, 166, 176)(146, 232, 233, 163, 217, 225)(148, 238, 150,
207, 168, 215)(151, 186, 170, 202, 216, 198)(162, 169, 213, 231, 209, 218)
d: (2, 5)(3, 9, 6, 18)(4, 13, 10, 29)(7, 20, 16, 44)(8, 24, 21, 56)(11, 31, 27,
64)(12, 35, 32, 70)(14, 39)(15, 43, 40, 57)(17, 47)(19, 51, 50, 94)(22, 58, 54,
100)(23, 46, 59, 55)(25, 62, 48, 83)(26, 63, 30, 49)(28, 66)(33, 71, 68,
110)(34, 74, 72, 98)(36, 78, 67, 109)(37, 81, 79, 92)(38, 85, 82, 118)(41, 52,
87, 91)(42, 73, 53, 99)(45, 86)(60, 105, 101, 114)(61, 93)(65, 107, 69, 90)(75,
77, 111, 84)(76, 106)(80, 117, 88, 102)(89, 95, 97, 119)(96, 113)(103, 104)(115,
116)(121, 134, 122, 163)(123, 208, 166, 221)(124, 200, 139, 169)(125, 129, 180,
206)(126, 240, 178, 239)(127, 146, 191, 205)(128, 217, 193, 219)(130, 148, 194,
235)(131, 190, 162, 170)(132, 188, 207, 140)(133, 214, 202, 199)(135, 168, 176,
220)(136, 184, 238, 171)(137, 142, 185, 237)(138, 201, 234, 144)(141, 186, 226,
175)(143, 236, 192, 232)(145, 195, 211, 155)(147, 158, 223, 215)(149, 230, 197,
161)(150, 183, 204, 224)(151, 229, 196, 213)(152, 174, 187, 210)(153, 172, 198,
164)(154, 231, 228, 212)(156, 233, 203, 165)(157, 182, 225, 167)(159, 181, 160,
222)(173, 218, 189, 177)(179, 209, 216, 227)
C4[ 240, 42 ]
240
-1 178 126 239 240
-2 134 178 126 163
-3 125 136 192 160
-4 125 192 204 217
-5 121 122 239 240
-6 143 180 159 238
-7 122 233 235 152
-8 189 127 150 164
-9 232 222 129 184
-10 143 180 150 219
-11 122 158 152 208
-12 189 127 227 207
-13 232 224 193 129
-14 143 134 192 163
-15 124 136 126 160
-16 121 165 187 148
-17 155 237 195 142
-18 181 236 171 206
-19 156 124 238 229
-20 203 130 163 174
-21 191 204 172 173
-22 215 128 228 131
-23 157 201 161 140
-24 177 146 183 153
-25 166 212 223 142
-26 235 203 139 141
-27 121 187 221 215
-28 155 157 225 195
-29 236 128 183 206
-30 156 124 148 226
-31 166 223 163 174
-32 132 209 191 173
-33 199 168 128 228
-34 211 201 140 218
-35 177 146 179 140
-36 135 212 191 142
-37 187 222 235 141
-38 155 189 204 217
-39 121 122 232 236
-40 178 159 139 238
-41 233 124 235 126
-42 123 125 150 164
-43 200 222 184 240
-44 210 134 156 194
-45 232 137 236 185
-46 132 234 149 182
-47 145 211 137 185
-48 231 123 147 237
-49 200 233 194 175
-50 136 213 203 139
-51 200 233 171 196
-52 200 203 130 240
-53 166 180 204 172
-54 154 158 193 162
-55 167 138 207 197
-56 198 224 205 218
-57 169 181 171 239
-58 190 212 147 217
-59 144 188 225 230
-60 176 133 234 230
-61 151 162 196 131
-62 154 221 215 185
-63 165 169 130 186
-64 210 123 134 147
-65 220 146 149 182
-66 145 167 211 182
-67 176 231 127 237
-68 154 220 214 193
-69 167 168 205 197
-70 188 205 216 218
-71 176 133 212 217
-72 144 177 188 145
-73 183 129 153 208
-74 132 155 189 234
-75 179 234 140 230
-76 198 162 131 153
-77 132 209 144 197
-78 154 168 205 185
-79 148 181 226 152
-80 166 136 180 213
-81 210 159 130 186
-82 150 173 195 219
-83 158 137 228 208
-84 201 149 227 207
-85 177 145 224 193
-86 143 192 237 142
-87 165 178 148 139
-88 123 125 238 229
-89 181 215 152 131
-90 176 157 127 161
-91 156 169 194 239
-92 160 194 174 175
-93 190 213 170 229
-94 165 169 151 184
-95 190 147 160 174
-96 213 229 175 186
-97 187 222 158 162
-98 138 173 195 207
-99 198 221 224 206
-100 231 223 170 219
-101 135 202 138 161
-102 171 129 196 208
-103 209 133 202 227
-104 199 179 214 216
-105 220 144 214 197
-106 190 170 172 164
-107 135 191 225 230
-108 167 157 225 182
-109 220 146 137 228
-110 231 135 202 219
-111 188 138 161 216
-112 209 179 216 227
-113 226 151 141 196
-114 199 168 201 149
-115 198 199 214 153
-116 133 202 172 164
-117 221 151 184 206
-118 211 128 183 218
-119 210 223 159 170
-120 226 141 175 186
-121 5 16 27 39
-122 11 5 39 7
-123 88 48 42 64
-124 15 19 30 41
-125 88 3 4 42
-126 1 2 15 41
-127 12 67 90 8
-128 22 33 29 118
-129 13 102 73 9
-130 81 52 63 20
-131 22 89 61 76
-132 77 46 74 32
-133 103 60 71 116
-134 44 2 14 64
-135 110 101 36 107
-136 3 80 15 50
-137 45 47 83 109
-138 55 111 101 98
-139 26 50 40 87
-140 23 34 35 75
-141 113 26 37 120
-142 25 36 17 86
-143 14 6 86 10
-144 77 59 72 105
-145 66 47 72 85
-146 24 35 65 109
-147 58 48 95 64
-148 79 16 30 87
-149 46 114 84 65
-150 82 8 42 10
-151 113 61 94 117
-152 11 89 79 7
-153 24 115 73 76
-154 78 68 62 54
-155 38 17 28 74
-156 44 91 19 30
-157 23 90 28 108
-158 11 83 97 54
-159 81 6 40 119
-160 3 15 92 95
-161 23 111 90 101
-162 61 97 54 76
-163 2 14 20 31
-164 116 106 8 42
-165 16 94 63 87
-166 25 80 31 53
-167 55 66 69 108
-168 33 78 69 114
-169 57 91 94 63
-170 100 93 106 119
-171 57 102 18 51
-172 116 106 53 21
-173 82 21 32 98
-174 92 95 20 31
-175 92 49 96 120
-176 67 90 60 71
-177 24 35 72 85
-178 1 2 40 87
-179 35 112 104 75
-180 80 6 53 10
-181 89 57 79 18
-182 66 46 108 65
-183 24 29 73 118
-184 94 117 9 43
-185 45 78 47 62
-186 81 63 96 120
-187 37 16 27 97
-188 111 59 70 72
-189 12 38 8 74
-190 58 93 95 106
-191 36 107 21 32
-192 3 14 4 86
-193 13 68 85 54
-194 44 91 92 49
-195 82 17 28 98
-196 102 113 61 51
-197 55 77 69 105
-198 99 56 115 76
-199 33 114 104 115
-200 49 51 52 43
-201 23 34 114 84
-202 110 101 103 116
-203 26 50 52 20
-204 4 38 53 21
-205 56 78 69 70
-206 99 18 29 117
-207 55 12 84 98
-208 11 102 83 73
-209 77 112 103 32
-210 44 81 64 119
-211 66 34 47 118
-212 25 36 58 71
-213 80 93 50 96
-214 68 104 115 105
-215 22 89 27 62
-216 111 112 70 104
-217 58 4 38 71
-218 34 56 70 118
-219 110 100 82 10
-220 68 105 65 109
-221 99 27 62 117
-222 37 9 97 43
-223 100 25 31 119
-224 99 56 13 85
-225 59 28 107 108
-226 79 113 30 120
-227 12 112 103 84
-228 22 33 83 109
-229 88 93 19 96
-230 59 60 107 75
-231 110 67 100 48
-232 45 13 39 9
-233 49 7 51 41
-234 46 60 74 75
-235 26 37 7 41
-236 45 39 18 29
-237 67 48 17 86
-238 88 6 40 19
-239 1 57 91 5
-240 1 5 52 43
0