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