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