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