Graph forms
for C4 [ 240, 137 ] =
PL(CS(Pr_10(1,1,2,2)[10^6],1))
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On this page are computer-accessible forms for the graph C4[ 240, 137 ] =
PL(CS(Pr_10(1,1,2,2)[10^6],1)).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {40, 121}, {39, 121}, {26, 127}, {25, 127}, {22, 126}, {22, 127},
{21, 127}, {21, 126}, {17, 125}, {18, 126}, {17, 126}, {18, 125}, {13, 125},
{10, 123}, {13, 124}, {9, 123}, {14, 124}, {14, 125}, {9, 124}, {10, 124}, {1,
121}, {2, 122}, {1, 122}, {2, 121}, {6, 122}, {6, 123}, {5, 123}, {5, 122}, {3,
131}, {4, 132}, {44, 172}, {95, 223}, {44, 173}, {68, 197}, {52, 181}, {94,
223}, {7, 133}, {68, 198}, {84, 214}, {7, 132}, {71, 196}, {84, 215}, {108,
239}, {22, 146}, {74, 206}, {73, 205}, {71, 195}, {65, 197}, {23, 147}, {24,
156}, {41, 173}, {46, 170}, {48, 180}, {22, 147}, {23, 146}, {24, 157}, {41,
172}, {46, 171}, {45, 171}, {51, 181}, {81, 215}, {105, 239}, {3, 132}, {74,
205}, {73, 206}, {65, 198}, {4, 131}, {45, 170}, {81, 214}, {15, 135}, {71,
207}, {21, 157}, {42, 162}, {43, 163}, {12, 133}, {70, 207}, {15, 134}, {21,
156}, {42, 163}, {43, 162}, {92, 213}, {96, 233}, {12, 134}, {92, 214}, {96,
234}, {72, 195}, {2, 142}, {72, 196}, {61, 177}, {8, 132}, {50, 190}, {89, 213},
{106, 230}, {3, 142}, {8, 133}, {11, 134}, {50, 191}, {107, 230}, {3, 141}, {11,
133}, {47, 161}, {49, 191}, {107, 229}, {2, 141}, {61, 178}, {49, 190}, {89,
214}, {106, 229}, {24, 136}, {91, 203}, {24, 137}, {72, 217}, {27, 138}, {48,
161}, {90, 203}, {27, 137}, {72, 218}, {4, 151}, {20, 135}, {75, 216}, {19,
135}, {31, 139}, {76, 216}, {28, 137}, {31, 138}, {87, 194}, {1, 151}, {115,
229}, {114, 228}, {70, 208}, {62, 168}, {16, 134}, {28, 138}, {87, 193}, {90,
204}, {16, 135}, {115, 228}, {114, 229}, {71, 208}, {63, 168}, {91, 204}, {46,
182}, {63, 167}, {47, 183}, {1, 152}, {62, 167}, {25, 128}, {46, 183}, {47,
182}, {88, 193}, {105, 240}, {26, 128}, {116, 238}, {88, 194}, {19, 136}, {116,
239}, {47, 180}, {76, 215}, {4, 152}, {69, 217}, {20, 136}, {29, 129}, {75,
215}, {108, 240}, {29, 128}, {23, 137}, {113, 239}, {30, 128}, {82, 204}, {83,
205}, {23, 136}, {113, 238}, {69, 218}, {30, 129}, {82, 205}, {83, 204}, {33,
129}, {60, 156}, {59, 155}, {34, 130}, {63, 158}, {76, 237}, {77, 236}, {63,
157}, {76, 238}, {8, 171}, {33, 130}, {34, 129}, {100, 199}, {6, 162}, {73,
237}, {8, 172}, {30, 186}, {31, 187}, {38, 130}, {40, 140}, {42, 142}, {7, 162},
{30, 187}, {31, 186}, {38, 131}, {42, 143}, {7, 161}, {37, 131}, {41, 143}, {77,
235}, {97, 199}, {6, 161}, {73, 238}, {60, 155}, {59, 156}, {37, 130}, {41,
142}, {25, 177}, {58, 146}, {57, 145}, {35, 139}, {36, 140}, {75, 227}, {5,
172}, {74, 227}, {61, 148}, {25, 176}, {97, 200}, {32, 138}, {62, 148}, {108,
198}, {112, 218}, {32, 139}, {58, 145}, {57, 146}, {39, 140}, {108, 199}, {112,
219}, {28, 176}, {78, 226}, {100, 200}, {107, 199}, {28, 177}, {62, 147}, {79,
226}, {107, 198}, {5, 171}, {74, 228}, {61, 147}, {79, 225}, {35, 140}, {36,
139}, {75, 228}, {78, 225}, {43, 153}, {88, 234}, {12, 191}, {43, 152}, {88,
235}, {104, 219}, {44, 152}, {93, 233}, {102, 210}, {104, 220}, {44, 153}, {103,
210}, {9, 191}, {117, 195}, {86, 224}, {87, 225}, {103, 209}, {109, 219}, {86,
225}, {117, 194}, {87, 224}, {93, 234}, {102, 209}, {109, 218}, {101, 220},
{120, 194}, {80, 235}, {120, 195}, {10, 182}, {26, 166}, {27, 167}, {80, 236},
{11, 182}, {26, 167}, {27, 166}, {11, 181}, {85, 235}, {94, 224}, {101, 219},
{110, 208}, {111, 209}, {10, 181}, {85, 234}, {95, 224}, {110, 209}, {111, 208},
{91, 154}, {79, 141}, {91, 153}, {16, 211}, {14, 202}, {16, 212}, {38, 226},
{39, 227}, {40, 236}, {15, 202}, {38, 227}, {39, 226}, {40, 237}, {92, 153},
{15, 201}, {92, 154}, {14, 201}, {37, 237}, {9, 192}, {57, 240}, {37, 236}, {89,
144}, {90, 144}, {12, 192}, {60, 240}, {18, 222}, {101, 169}, {19, 222}, {101,
168}, {19, 221}, {119, 185}, {118, 184}, {102, 168}, {18, 221}, {119, 184},
{118, 185}, {102, 169}, {56, 232}, {56, 233}, {96, 179}, {96, 180}, {113, 165},
{103, 179}, {105, 189}, {90, 143}, {103, 178}, {105, 188}, {113, 164}, {89,
143}, {114, 164}, {106, 188}, {106, 189}, {119, 160}, {114, 165}, {29, 197},
{120, 160}, {78, 150}, {13, 212}, {29, 196}, {78, 151}, {77, 151}, {116, 174},
{104, 178}, {77, 150}, {116, 175}, {104, 179}, {53, 233}, {115, 175}, {59, 231},
{58, 230}, {98, 190}, {53, 232}, {115, 174}, {64, 157}, {59, 230}, {58, 231},
{80, 141}, {99, 190}, {13, 211}, {64, 158}, {99, 189}, {98, 189}, {52, 212},
{118, 150}, {117, 149}, {52, 213}, {60, 221}, {86, 183}, {85, 183}, {117, 150},
{118, 149}, {32, 196}, {66, 166}, {65, 165}, {57, 221}, {56, 220}, {54, 210},
{49, 213}, {32, 197}, {54, 211}, {49, 212}, {53, 211}, {53, 210}, {120, 159},
{66, 165}, {65, 166}, {54, 222}, {119, 159}, {55, 223}, {54, 223}, {55, 222},
{55, 220}, {68, 175}, {95, 180}, {34, 206}, {67, 175}, {35, 207}, {45, 193},
{95, 179}, {34, 207}, {35, 206}, {45, 192}, {85, 184}, {86, 184}, {112, 158},
{79, 160}, {112, 159}, {48, 192}, {80, 160}, {97, 145}, {111, 159}, {48, 193},
{64, 177}, {56, 201}, {82, 163}, {97, 144}, {111, 158}, {64, 178}, {81, 163},
{98, 144}, {20, 231}, {67, 176}, {98, 145}, {68, 176}, {93, 169}, {94, 170},
{81, 164}, {17, 231}, {82, 164}, {93, 170}, {94, 169}, {33, 217}, {67, 187},
{51, 203}, {50, 202}, {99, 155}, {109, 149}, {17, 232}, {66, 187}, {51, 202},
{33, 216}, {50, 203}, {84, 173}, {99, 154}, {109, 148}, {84, 174}, {110, 148},
{51, 200}, {110, 149}, {20, 232}, {70, 186}, {69, 185}, {52, 200}, {36, 216},
{36, 217}, {83, 174}, {55, 201}, {66, 188}, {83, 173}, {100, 154}, {67, 188},
{70, 185}, {69, 186}, {100, 155} }>;
(II) A more general form is to represent the graph as the orbit of {40, 121}
under the group generated by the following permutations:
a: (17, 18)(19, 20)(37, 38)(39, 40)(53, 54)(55, 56)(57, 58)(59, 60)(73, 74)(75,
76)(77, 78)(79, 80)(85, 86)(87, 88)(93, 94)(95, 96)(105, 106)(107, 108)(113,
114)(115, 116)(221, 231)(222, 232)(223, 233)(224, 234)(225, 235)(226, 236)(227,
237)(228, 238)(229, 239)(230, 240) (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, 5, 9, 13, 18, 21, 26, 30, 34, 37, 3, 7, 11, 15, 20, 23, 28, 32, 36,
39)(2, 6, 10, 14, 17, 22, 25, 29, 33, 38, 4, 8, 12, 16, 19, 24, 27, 31, 35,
40)(41, 48, 52, 55, 59, 62, 67, 71, 76, 79, 43, 46, 50, 53, 57, 64, 65, 69, 74,
77)(42, 47, 51, 56, 58, 61, 68, 72, 75, 78, 44, 45, 49, 54, 60, 63, 66, 70, 73,
80)(81, 86, 91, 93, 98, 103, 108, 112, 114, 118, 83, 88, 89, 95, 100, 101, 106,
110, 116, 120)(82, 85, 90, 96, 97, 104, 107, 109, 115, 117, 84, 87, 92, 94, 99,
102, 105, 111, 113, 119)(121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 140)(141, 162, 182, 202, 232, 146, 177,
197, 217, 227, 151, 172, 192, 212, 222, 156, 167, 187, 207, 237)(142, 161, 181,
201, 231, 147, 176, 196, 216, 226, 152, 171, 191, 211, 221, 157, 166, 186, 206,
236)(143, 180, 200, 220, 230, 148, 175, 195, 215, 225, 153, 170, 190, 210, 240,
158, 165, 185, 205, 235)(144, 179, 199, 219, 229, 149, 174, 194, 214, 224, 154,
169, 189, 209, 239, 159, 164, 184, 204, 234)(145, 178, 198, 218, 228, 150, 173,
193, 213, 223, 155, 168, 188, 208, 238, 160, 163, 183, 203, 233)
c: (9, 10)(11, 12)(29, 30)(31, 32)(45, 46)(47, 48)(49, 52)(50, 51)(65, 66)(67,
68)(69, 72)(70, 71)(85, 88)(86, 87)(97, 98)(99, 100)(105, 108)(106, 107)(117,
118)(119, 120)(181, 191)(182, 192)(183, 193)(184, 194)(185, 195)(186, 196)(187,
197)(188, 198)(189, 199)(190, 200)
d: (1, 2)(3, 4)(21, 22)(23, 24)(41, 44)(42, 43)(57, 60)(58, 59)(61, 64)(62,
63)(77, 80)(78, 79)(89, 92)(90, 91)(97, 100)(98, 99)(109, 112)(110, 111)(117,
120)(118, 119)(141, 151)(142, 152)(143, 153)(144, 154)(145, 155)(146, 156)(147,
157)(148, 158)(149, 159)(150, 160)
e: (5, 6)(7, 8)(25, 26)(27, 28)(41, 42)(43, 44)(45, 48)(46, 47)(61, 62)(63,
64)(65, 68)(66, 67)(81, 84)(82, 83)(93, 96)(94, 95)(101, 104)(102, 103)(113,
116)(114, 115)(161, 171)(162, 172)(163, 173)(164, 174)(165, 175)(166, 176)(167,
177)(168, 178)(169, 179)(170, 180)
f: (2, 4)(5, 78, 6, 77)(7, 80, 8, 79)(9, 118)(10, 117)(11, 120)(12, 119)(13,
109)(14, 110)(15, 111)(16, 112)(17, 62, 18, 61)(19, 64, 20, 63)(21, 23)(25, 58,
26, 57)(27, 60, 28, 59)(29, 97)(30, 98)(31, 99)(32, 100)(33, 89)(34, 90)(35,
91)(36, 92)(37, 41, 38, 42)(39, 43, 40, 44)(45, 86, 48, 85)(46, 87, 47, 88)(49,
69)(50, 70)(51, 71)(52, 72)(53, 101, 54, 104)(55, 103, 56, 102)(65, 108, 68,
107)(66, 105, 67, 106)(73, 83, 74, 82)(75, 81, 76, 84)(93, 94, 95, 96)(113, 116,
115, 114)(121, 152)(122, 151)(123, 150)(124, 149)(125, 148)(126, 147)(127,
146)(128, 145)(129, 144)(130, 143)(131, 142)(132, 141)(133, 160)(134, 159)(135,
158)(136, 157)(137, 156)(138, 155)(139, 154)(140, 153)(161, 235, 171, 225)(162,
236, 172, 226)(163, 237, 173, 227)(164, 238, 174, 228)(165, 239, 175, 229)(166,
240, 176, 230)(167, 221, 177, 231)(168, 222, 178, 232)(169, 223, 179, 233)(170,
224, 180, 234)(181, 195)(182, 194)(183, 193)(184, 192)(185, 191)(186, 190)(187,
189)(196, 200)(197, 199)(201, 209)(202, 208)(203, 207)(204, 206)(210, 220)(211,
219)(212, 218)(213, 217)(214, 216)
g: (13, 14)(15, 16)(17, 18)(19, 20)(33, 34)(35, 36)(37, 38)(39, 40)(49, 50)(51,
52)(53, 55)(54, 56)(57, 58)(59, 60)(69, 70)(71, 72)(73, 75)(74, 76)(77, 78)(79,
80)(81, 82)(83, 84)(85, 86)(87, 88)(89, 90)(91, 92)(93, 94)(95, 96)(101,
102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 114)(115, 116)(201,
211)(202, 212)(203, 213)(204, 214)(205, 215)(206, 216)(207, 217)(208, 218)(209,
219)(210, 220)(221, 231)(222, 232)(223, 233)(224, 234)(225, 235)(226, 236)(227,
237)(228, 238)(229, 239)(230, 240)
h: (5, 39)(6, 40)(7, 37)(8, 38)(9, 35, 10, 36)(11, 33, 12, 34)(13, 32, 14,
31)(15, 30, 16, 29)(17, 27)(18, 28)(19, 25)(20, 26)(21, 23)(22, 24)(41, 79)(42,
80)(43, 77)(44, 78)(45, 74, 46, 75)(47, 76, 48, 73)(49, 71, 51, 69)(50, 70, 52,
72)(53, 65, 56, 66)(54, 68, 55, 67)(57, 64)(58, 63)(59, 62)(60, 61)(81, 88, 82,
85)(83, 86, 84, 87)(89, 120, 90, 119)(91, 118, 92, 117)(93, 114)(94, 115)(95,
116)(96, 113)(97, 112, 98, 111)(99, 110, 100, 109)(101, 106, 102, 107)(103, 108,
104, 105)(121, 122)(123, 140)(124, 139)(125, 138)(126, 137)(127, 136)(128,
135)(129, 134)(130, 133)(131, 132)(141, 142)(143, 160)(144, 159)(145, 158)(146,
157)(147, 156)(148, 155)(149, 154)(150, 153)(151, 152)(161, 237)(162, 236)(163,
235)(164, 234)(165, 233)(166, 232)(167, 231)(168, 230)(169, 229)(170, 228)(171,
227)(172, 226)(173, 225)(174, 224)(175, 223)(176, 222)(177, 221)(178, 240)(179,
239)(180, 238)(181, 217, 191, 207)(182, 216, 192, 206)(183, 215, 193, 205)(184,
214, 194, 204)(185, 213, 195, 203)(186, 212, 196, 202)(187, 211, 197, 201)(188,
210, 198, 220)(189, 209, 199, 219)(190, 208, 200, 218)
C4[ 240, 137 ]
240
-1 121 122 151 152
-2 121 122 141 142
-3 132 141 131 142
-4 132 151 152 131
-5 122 123 171 172
-6 122 123 161 162
-7 132 133 161 162
-8 132 133 171 172
-9 123 124 191 192
-10 123 124 181 182
-11 133 134 181 182
-12 133 134 191 192
-13 211 124 212 125
-14 124 201 125 202
-15 134 135 201 202
-16 134 211 135 212
-17 231 232 125 126
-18 221 222 125 126
-19 221 222 135 136
-20 231 232 135 136
-21 156 157 126 127
-22 146 147 126 127
-23 146 136 147 137
-24 156 157 136 137
-25 176 177 127 128
-26 166 167 127 128
-27 166 167 137 138
-28 176 177 137 138
-29 128 129 196 197
-30 187 128 129 186
-31 187 138 139 186
-32 138 139 196 197
-33 216 129 217 130
-34 129 206 130 207
-35 139 140 206 207
-36 139 216 140 217
-37 236 237 130 131
-38 226 227 130 131
-39 121 226 227 140
-40 121 236 237 140
-41 143 172 173 142
-42 143 162 163 142
-43 162 152 163 153
-44 172 173 152 153
-45 170 192 171 193
-46 170 171 182 183
-47 180 182 161 183
-48 180 192 193 161
-49 190 212 191 213
-50 190 191 202 203
-51 200 202 181 203
-52 200 212 213 181
-53 210 232 211 233
-54 210 211 222 223
-55 220 222 201 223
-56 220 232 233 201
-57 221 145 146 240
-58 231 145 146 230
-59 231 155 156 230
-60 155 221 156 240
-61 177 178 147 148
-62 167 168 147 148
-63 167 157 168 158
-64 177 178 157 158
-65 165 198 166 197
-66 165 187 166 188
-67 176 187 188 175
-68 176 198 175 197
-69 217 185 218 186
-70 185 207 186 208
-71 195 196 207 208
-72 195 217 196 218
-73 237 205 238 206
-74 205 227 206 228
-75 215 216 227 228
-76 215 237 216 238
-77 235 236 150 151
-78 225 226 150 151
-79 225 160 226 141
-80 235 236 160 141
-81 214 215 163 164
-82 204 205 163 164
-83 204 205 173 174
-84 214 215 173 174
-85 234 235 183 184
-86 224 225 183 184
-87 224 225 193 194
-88 234 235 193 194
-89 143 144 213 214
-90 143 144 203 204
-91 154 203 204 153
-92 154 213 214 153
-93 233 234 169 170
-94 223 169 224 170
-95 179 223 180 224
-96 233 179 234 180
-97 144 199 145 200
-98 144 145 189 190
-99 154 155 189 190
-100 154 155 199 200
-101 220 168 169 219
-102 209 210 168 169
-103 209 210 178 179
-104 220 178 179 219
-105 188 189 239 240
-106 188 189 229 230
-107 198 199 229 230
-108 198 199 239 240
-109 148 149 218 219
-110 209 148 149 208
-111 209 158 159 208
-112 158 159 218 219
-113 165 238 239 164
-114 165 228 229 164
-115 228 174 229 175
-116 238 239 174 175
-117 149 150 194 195
-118 149 150 184 185
-119 159 160 184 185
-120 159 160 194 195
-121 1 2 39 40
-122 1 2 5 6
-123 5 6 9 10
-124 13 14 9 10
-125 13 14 17 18
-126 22 17 18 21
-127 22 25 26 21
-128 25 26 29 30
-129 33 34 29 30
-130 33 34 37 38
-131 3 4 37 38
-132 3 4 7 8
-133 11 12 7 8
-134 11 12 15 16
-135 15 16 19 20
-136 23 24 19 20
-137 23 24 27 28
-138 27 28 31 32
-139 35 36 31 32
-140 35 36 39 40
-141 2 79 3 80
-142 2 3 41 42
-143 89 90 41 42
-144 89 90 97 98
-145 57 58 97 98
-146 22 23 57 58
-147 22 23 61 62
-148 110 61 62 109
-149 110 117 118 109
-150 77 78 117 118
-151 77 1 78 4
-152 44 1 4 43
-153 44 91 92 43
-154 99 100 91 92
-155 99 100 59 60
-156 24 59 60 21
-157 24 63 64 21
-158 111 112 63 64
-159 111 112 119 120
-160 79 80 119 120
-161 47 48 6 7
-162 6 7 42 43
-163 81 82 42 43
-164 113 81 114 82
-165 66 113 114 65
-166 66 26 27 65
-167 26 27 62 63
-168 101 102 62 63
-169 101 102 93 94
-170 45 46 93 94
-171 45 46 5 8
-172 44 5 8 41
-173 44 83 84 41
-174 115 83 116 84
-175 67 68 115 116
-176 67 68 25 28
-177 25 28 61 64
-178 103 104 61 64
-179 103 104 95 96
-180 47 48 95 96
-181 11 51 52 10
-182 11 46 47 10
-183 46 47 85 86
-184 85 118 86 119
-185 69 70 118 119
-186 69 70 30 31
-187 66 67 30 31
-188 66 67 105 106
-189 99 105 106 98
-190 99 49 50 98
-191 12 49 50 9
-192 12 45 48 9
-193 88 45 48 87
-194 88 117 87 120
-195 71 72 117 120
-196 71 72 29 32
-197 68 29 32 65
-198 68 107 108 65
-199 100 107 97 108
-200 100 51 52 97
-201 55 56 14 15
-202 14 15 50 51
-203 90 91 50 51
-204 90 91 82 83
-205 82 83 73 74
-206 34 35 73 74
-207 34 35 70 71
-208 110 111 70 71
-209 110 111 102 103
-210 102 103 53 54
-211 13 16 53 54
-212 13 16 49 52
-213 89 92 49 52
-214 89 81 92 84
-215 81 84 75 76
-216 33 36 75 76
-217 33 36 69 72
-218 112 69 72 109
-219 101 112 104 109
-220 55 56 101 104
-221 57 60 18 19
-222 55 18 19 54
-223 55 94 95 54
-224 94 95 86 87
-225 78 79 86 87
-226 78 79 38 39
-227 38 39 74 75
-228 114 115 74 75
-229 114 115 106 107
-230 58 59 106 107
-231 58 59 17 20
-232 56 17 20 53
-233 56 93 96 53
-234 88 93 85 96
-235 77 88 80 85
-236 77 80 37 40
-237 37 40 73 76
-238 113 116 73 76
-239 113 105 116 108
-240 57 60 105 108
0