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