Graph forms
for C4 [ 256, 126 ] =
BGCG({4,4}_8,0;K2;{12,15,17,19})
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On this page are computer-accessible forms for the graph C4[ 256, 126 ] =
BGCG({4,4}_8,0;K2;{12,15,17,19}).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {128, 137}, {128, 167}, {128, 171}, {128, 213}, {8, 136}, {116,
244}, {113, 241}, {108, 236}, {18, 146}, {70, 198}, {71, 198}, {109, 236}, {102,
231}, {94, 223}, {86, 215}, {28, 158}, {126, 252}, {125, 255}, {124, 254}, {17,
146}, {112, 243}, {104, 235}, {55, 180}, {33, 162}, {74, 201}, {54, 178}, {63,
186}, {99, 229}, {101, 227}, {81, 214}, {115, 244}, {100, 227}, {51, 187}, {94,
215}, {120, 241}, {110, 231}, {4, 142}, {117, 255}, {116, 254}, {97, 235}, {16,
155}, {31, 148}, {22, 154}, {58, 182}, {39, 171}, {26, 150}, {65, 205}, {78,
194}, {40, 165}, {105, 228}, {83, 222}, {75, 197}, {124, 242}, {107, 229}, {7,
136}, {125, 242}, {89, 214}, {57, 182}, {25, 150}, {21, 154}, {9, 134}, {74,
197}, {9, 153}, {101, 245}, {43, 187}, {40, 185}, {120, 233}, {82, 192}, {8,
155}, {10, 153}, {12, 152}, {112, 228}, {95, 203}, {91, 207}, {90, 206}, {42,
190}, {78, 218}, {86, 194}, {13, 152}, {48, 165}, {43, 190}, {75, 222}, {1,
151}, {27, 141}, {64, 214}, {17, 134}, {39, 176}, {63, 168}, {69, 210}, {40,
176}, {109, 245}, {96, 248}, {32, 185}, {112, 233}, {93, 196}, {61, 164}, {39,
189}, {94, 196}, {90, 192}, {62, 164}, {38, 189}, {58, 161}, {47, 180}, {82,
201}, {13, 145}, {111, 243}, {46, 178}, {70, 218}, {83, 207}, {87, 203}, {125,
224}, {3, 157}, {101, 251}, {8, 151}, {14, 145}, {77, 210}, {88, 199}, {23,
183}, {93, 253}, {2, 163}, {98, 195}, {89, 248}, {22, 183}, {79, 238}, {81,
240}, {1, 163}, {114, 208}, {97, 195}, {26, 184}, {12, 174}, {85, 247}, {2,
161}, {105, 202}, {27, 184}, {16, 179}, {4, 167}, {3, 160}, {84, 247}, {3, 167},
{119, 211}, {21, 177}, {14, 170}, {8, 172}, {66, 230}, {11, 174}, {26, 191},
{15, 170}, {69, 224}, {79, 234}, {59, 157}, {93, 251}, {1, 166}, {127, 216},
{96, 199}, {79, 232}, {20, 188}, {85, 253}, {88, 240}, {80, 249}, {116, 221},
{3, 169}, {122, 208}, {2, 169}, {120, 211}, {24, 179}, {11, 160}, {45, 129},
{109, 193}, {98, 206}, {74, 230}, {18, 191}, {120, 213}, {35, 141}, {9, 166},
{119, 216}, {46, 129}, {42, 133}, {71, 232}, {5, 181}, {59, 139}, {51, 131},
{50, 130}, {37, 149}, {35, 147}, {12, 188}, {73, 249}, {82, 226}, {50, 131},
{121, 200}, {108, 221}, {58, 139}, {83, 226}, {60, 142}, {126, 204}, {93, 239},
{68, 246}, {6, 181}, {92, 239}, {57, 138}, {49, 130}, {38, 149}, {28, 175}, {27,
175}, {121, 205}, {117, 193}, {111, 219}, {32, 148}, {31, 171}, {24, 173}, {110,
219}, {100, 209}, {42, 159}, {41, 156}, {111, 217}, {36, 147}, {50, 133}, {108,
212}, {41, 144}, {113, 200}, {102, 223}, {54, 143}, {84, 237}, {23, 173}, {118,
204}, {54, 140}, {53, 143}, {42, 144}, {36, 158}, {62, 132}, {70, 252}, {76,
246}, {25, 162}, {113, 202}, {60, 135}, {55, 140}, {63, 132}, {13, 177}, {59,
135}, {53, 137}, {7, 186}, {108, 209}, {52, 137}, {34, 159}, {33, 156}, {87,
234}, {68, 250}, {103, 217}, {98, 220}, {95, 225}, {80, 238}, {83, 237}, {69,
250}, {107, 212}, {99, 220}, {94, 225}, {10, 202}, {97, 161}, {51, 243}, {36,
228}, {71, 135}, {81, 145}, {37, 228}, {92, 157}, {60, 253}, {7, 197}, {98,
160}, {6, 197}, {49, 242}, {19, 208}, {82, 145}, {17, 213}, {123, 191}, {119,
179}, {48, 244}, {40, 236}, {35, 230}, {62, 251}, {30, 216}, {127, 185}, {46,
232}, {45, 235}, {38, 224}, {44, 235}, {118, 177}, {104, 175}, {52, 243}, {103,
175}, {52, 253}, {68, 141}, {41, 227}, {106, 160}, {56, 242}, {64, 138}, {27,
208}, {103, 172}, {10, 198}, {121, 181}, {115, 191}, {95, 147}, {89, 149}, {25,
213}, {61, 241}, {73, 133}, {80, 156}, {85, 153}, {11, 198}, {60, 241}, {43,
230}, {33, 236}, {19, 221}, {104, 166}, {38, 232}, {22, 216}, {1, 206}, {122,
181}, {115, 188}, {90, 149}, {14, 193}, {72, 135}, {86, 153}, {24, 200}, {72,
152}, {74, 154}, {56, 234}, {104, 186}, {31, 204}, {48, 227}, {37, 246}, {73,
154}, {5, 209}, {72, 156}, {75, 159}, {81, 133}, {91, 142}, {11, 221}, {112,
166}, {107, 189}, {14, 217}, {107, 188}, {106, 189}, {32, 247}, {26, 205}, {22,
193}, {18, 202}, {127, 167}, {122, 162}, {102, 190}, {37, 252}, {103, 190}, {65,
152}, {5, 223}, {96, 186}, {48, 234}, {77, 151}, {23, 204}, {47, 244}, {45,
246}, {76, 151}, {13, 209}, {111, 179}, {67, 159}, {78, 146}, {30, 195}, {126,
163}, {67, 158}, {29, 195}, {125, 163}, {6, 217}, {110, 177}, {77, 146}, {7,
231}, {55, 215}, {41, 201}, {66, 162}, {29, 252}, {76, 173}, {15, 237}, {61,
223}, {28, 255}, {55, 212}, {29, 254}, {72, 171}, {65, 165}, {80, 180}, {33,
196}, {123, 158}, {117, 144}, {106, 143}, {65, 164}, {15, 233}, {118, 144},
{105, 143}, {34, 196}, {66, 164}, {75, 173}, {79, 169}, {2, 229}, {78, 169},
{85, 178}, {15, 231}, {32, 200}, {63, 215}, {64, 168}, {66, 170}, {67, 170},
{16, 250}, {52, 222}, {20, 255}, {91, 176}, {21, 254}, {67, 168}, {20, 248},
{110, 130}, {106, 134}, {92, 176}, {91, 183}, {56, 212}, {28, 240}, {64, 172},
{68, 168}, {73, 165}, {88, 180}, {21, 248}, {99, 142}, {90, 183}, {29, 240},
{25, 247}, {56, 214}, {86, 184}, {10, 229}, {109, 130}, {45, 194}, {34, 205},
{84, 187}, {87, 184}, {70, 182}, {121, 137}, {113, 129}, {102, 150}, {100, 148},
{4, 245}, {124, 141}, {19, 225}, {105, 155}, {46, 220}, {44, 222}, {9, 250},
{123, 136}, {114, 129}, {101, 150}, {96, 147}, {95, 172}, {51, 192}, {47, 220},
{18, 225}, {69, 182}, {114, 134}, {124, 136}, {47, 218}, {58, 207}, {62, 203},
{36, 210}, {122, 140}, {114, 132}, {49, 199}, {88, 174}, {24, 239}, {123, 140},
{115, 132}, {99, 148}, {57, 206}, {53, 194}, {76, 187}, {35, 219}, {89, 161},
{49, 201}, {43, 211}, {12, 245}, {100, 157}, {34, 219}, {87, 174}, {20, 238},
{97, 155}, {59, 192}, {5, 249}, {127, 131}, {119, 139}, {30, 226}, {4, 249},
{126, 131}, {118, 139}, {54, 203}, {50, 207}, {39, 218}, {31, 226}, {19, 238},
{16, 237}, {6, 251}, {17, 239}, {116, 138}, {57, 199}, {44, 210}, {30, 224},
{23, 233}, {71, 185}, {44, 211}, {117, 138}, {77, 178}, {53, 256}, {61, 256},
{84, 256}, {92, 256} }>;
(II) A more general form is to represent the graph as the orbit of {128, 137}
under the group generated by the following permutations:
a: (2, 98)(3, 99)(6, 102)(7, 103)(10, 106)(11, 107)(14, 110)(15, 111)(17,
85)(18, 54)(19, 55)(20, 88)(21, 81)(22, 50)(23, 51)(24, 84)(25, 93)(26, 62)(27,
63)(28, 96)(29, 89)(30, 58)(31, 59)(32, 92)(34, 66)(35, 67)(38, 70)(39, 71)(42,
74)(43, 75)(46, 78)(47, 79)(49, 117)(52, 120)(53, 113)(56, 116)(57, 125)(60,
128)(61, 121)(64, 124)(82, 118)(83, 119)(86, 114)(87, 115)(90, 126)(91, 127)(94,
122)(95, 123)(129, 194)(130, 193)(131, 183)(132, 184)(133, 154)(134, 153)(135,
171)(136, 172)(137, 241)(138, 242)(139, 226)(140, 225)(141, 168)(142, 167)(143,
202)(144, 201)(145, 177)(146, 178)(147, 158)(148, 157)(149, 252)(150, 251)(159,
230)(160, 229)(161, 195)(162, 196)(163, 206)(164, 205)(169, 220)(170, 219)(173,
187)(174, 188)(175, 186)(176, 185)(179, 237)(180, 238)(181, 223)(182, 224)(189,
198)(190, 197)(191, 203)(192, 204)(199, 255)(200, 256)(207, 216)(208, 215)(211,
222)(212, 221)(213, 253)(214, 254)(217, 231)(218, 232)(233, 243)(234, 244)(239,
247)(240, 248) (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, 8)(4, 7)(5, 6)(9, 10)(11, 16)(12, 15)(13, 14)(17, 18)(19, 24)(20,
23)(21, 22)(25, 26)(27, 32)(28, 31)(29, 30)(33, 34)(35, 40)(36, 39)(37, 38)(41,
42)(43, 48)(44, 47)(45, 46)(49, 50)(51, 56)(52, 55)(53, 54)(57, 58)(59, 64)(60,
63)(61, 62)(65, 66)(67, 72)(68, 71)(69, 70)(73, 74)(75, 80)(76, 79)(77, 78)(81,
82)(83, 88)(84, 87)(85, 86)(89, 90)(91, 96)(92, 95)(93, 94)(97, 98)(99,
104)(100, 103)(101, 102)(105, 106)(107, 112)(108, 111)(109, 110)(113, 114)(115,
120)(116, 119)(117, 118)(121, 122)(123, 128)(124, 127)(125, 126)(131, 242)(132,
241)(133, 201)(134, 202)(135, 168)(136, 167)(137, 140)(138, 139)(141, 185)(142,
186)(147, 176)(148, 175)(151, 169)(152, 170)(155, 160)(156, 159)(157, 172)(158,
171)(161, 206)(162, 205)(165, 230)(166, 229)(173, 238)(174, 237)(177, 193)(178,
194)(179, 221)(180, 222)(183, 248)(184, 247)(187, 234)(188, 233)(189, 228)(190,
227)(191, 213)(192, 214)(197, 249)(198, 250)(199, 207)(200, 208)(203, 256)(204,
255)(209, 217)(210, 218)(211, 244)(212, 243)(215, 253)(216, 254)(219, 236)(220,
235)(223, 251)(224, 252)(225, 239)(226, 240)(231, 245)(232, 246)
c: (2, 104, 98, 8)(3, 103)(4, 6, 100, 102)(7, 99)(9, 57, 77, 125)(10, 96, 46,
124)(11, 95, 79, 27)(12, 62, 48, 26)(13, 61, 73, 121)(14, 92, 42, 128)(15, 91,
75, 31)(16, 58, 44, 30)(17, 117)(18, 20, 114, 116)(21, 113)(22, 24, 118,
120)(25, 109, 93, 41)(28, 106, 64, 78)(29, 105, 89, 45)(32, 110, 60, 74)(34, 72,
66, 40)(35, 71)(36, 38, 68, 70)(39, 67)(43, 127, 111, 59)(47, 123, 107, 63)(49,
85)(50, 52, 82, 84)(53, 81)(54, 56, 86, 88)(76, 126, 112, 90)(80, 122, 108,
94)(129, 254, 202, 248)(130, 253, 201, 247)(131, 243, 192, 187)(132, 244, 191,
188)(133, 137, 145, 256)(134, 138, 146, 255)(135, 230, 185, 219)(136, 229, 186,
220)(139, 211, 216, 179)(140, 212, 215, 180)(141, 198, 147, 232)(142, 197, 148,
231)(143, 214, 194, 240)(144, 213, 193, 239)(149, 246, 252, 228)(150, 245, 251,
227)(151, 163, 166, 206)(152, 164, 165, 205)(153, 199, 178, 242)(154, 200, 177,
241)(155, 161, 235, 195)(156, 162, 236, 196)(157, 190, 167, 217)(158, 189, 168,
218)(159, 171, 170, 176)(160, 172, 169, 175)(173, 204, 233, 183)(174, 203, 234,
184)(181, 209, 223, 249)(182, 210, 224, 250)(207, 222, 226, 237)(208, 221, 225,
238)
d: (2, 9)(3, 17)(4, 25)(5, 33)(6, 41)(7, 49)(8, 57)(11, 18)(12, 26)(13, 34)(14,
42)(15, 50)(16, 58)(20, 27)(21, 35)(22, 43)(23, 51)(24, 59)(29, 36)(30, 44)(31,
52)(32, 60)(38, 45)(39, 53)(40, 61)(47, 54)(48, 62)(56, 63)(66, 73)(67, 81)(68,
89)(69, 97)(70, 105)(71, 113)(72, 121)(75, 82)(76, 90)(77, 98)(78, 106)(79,
114)(80, 122)(84, 91)(85, 99)(86, 107)(87, 115)(88, 123)(93, 100)(94, 108)(95,
116)(96, 124)(102, 109)(103, 117)(104, 125)(111, 118)(112, 126)(120, 127)(129,
232)(130, 231)(131, 233)(132, 234)(133, 170)(134, 169)(135, 200)(136, 199)(137,
171)(138, 172)(139, 179)(140, 180)(141, 248)(142, 247)(143, 218)(144, 217)(145,
159)(146, 160)(147, 254)(148, 253)(149, 246)(150, 245)(151, 206)(152, 205)(153,
229)(154, 230)(155, 182)(156, 181)(157, 239)(158, 240)(161, 250)(162, 249)(163,
166)(164, 165)(167, 213)(168, 214)(173, 192)(174, 191)(175, 255)(176, 256)(177,
219)(178, 220)(183, 187)(184, 188)(185, 241)(186, 242)(189, 194)(190, 193)(195,
210)(196, 209)(197, 201)(198, 202)(203, 244)(204, 243)(207, 237)(208, 238)(211,
216)(212, 215)(221, 225)(222, 226)(223, 236)(224, 235)(227, 251)(228, 252)
C4[ 256, 126 ]
256
-1 166 151 206 163
-2 169 161 163 229
-3 167 157 169 160
-4 167 245 249 142
-5 209 223 181 249
-6 181 217 251 197
-7 231 136 186 197
-8 155 136 172 151
-9 166 134 250 153
-10 198 202 229 153
-11 198 221 160 174
-12 188 245 152 174
-13 209 177 145 152
-14 145 170 193 217
-15 231 233 170 237
-16 155 179 237 250
-17 134 146 213 239
-18 146 191 202 225
-19 221 225 238 208
-20 188 255 248 238
-21 154 177 254 248
-22 154 193 183 216
-23 233 204 183 173
-24 200 179 173 239
-25 213 247 150 162
-26 191 150 205 184
-27 184 141 175 208
-28 255 158 240 175
-29 254 195 240 252
-30 224 226 216 195
-31 148 171 204 226
-32 200 148 247 185
-33 156 236 162 196
-34 159 205 196 219
-35 147 141 219 230
-36 210 147 158 228
-37 246 149 228 252
-38 232 189 224 149
-39 176 189 171 218
-40 165 176 236 185
-41 144 156 201 227
-42 133 144 190 159
-43 187 211 190 230
-44 210 211 222 235
-45 235 246 194 129
-46 220 232 178 129
-47 220 244 180 218
-48 165 244 234 227
-49 242 199 201 130
-50 133 130 207 131
-51 187 243 192 131
-52 253 243 222 137
-53 143 256 137 194
-54 143 178 203 140
-55 212 180 215 140
-56 242 212 234 214
-57 199 138 182 206
-58 182 139 161 207
-59 135 157 192 139
-60 253 135 142 241
-61 223 256 164 241
-62 132 203 251 164
-63 132 168 215 186
-64 168 214 138 172
-65 165 205 152 164
-66 170 162 164 230
-67 168 158 159 170
-68 168 246 250 141
-69 210 224 182 250
-70 198 182 218 252
-71 198 232 135 185
-72 156 135 171 152
-73 154 165 133 249
-74 154 201 197 230
-75 222 159 173 197
-76 187 246 151 173
-77 210 178 146 151
-78 146 169 194 218
-79 232 234 169 238
-80 156 180 238 249
-81 133 145 214 240
-82 145 201 192 226
-83 222 226 237 207
-84 187 256 247 237
-85 253 178 247 153
-86 215 194 184 153
-87 234 203 184 174
-88 199 180 174 240
-89 214 149 248 161
-90 192 149 183 206
-91 176 183 207 142
-92 176 157 256 239
-93 253 239 196 251
-94 223 225 215 196
-95 147 203 225 172
-96 199 147 248 186
-97 155 235 161 195
-98 220 160 195 206
-99 220 148 229 142
-100 209 157 148 227
-101 245 150 227 251
-102 231 190 223 150
-103 190 172 217 175
-104 166 235 175 186
-105 143 155 202 228
-106 143 134 189 160
-107 188 189 212 229
-108 209 221 212 236
-109 245 236 193 130
-110 231 177 130 219
-111 243 179 217 219
-112 166 243 233 228
-113 200 202 129 241
-114 132 134 129 208
-115 132 188 244 191
-116 221 254 244 138
-117 144 255 138 193
-118 144 177 204 139
-119 211 179 139 216
-120 211 233 213 241
-121 200 137 181 205
-122 181 140 162 208
-123 136 158 191 140
-124 242 254 136 141
-125 242 255 224 163
-126 204 163 131 252
-127 167 216 185 131
-128 167 213 137 171
-129 45 46 113 114
-130 110 49 50 109
-131 126 50 127 51
-132 114 115 62 63
-133 81 50 73 42
-134 114 17 106 9
-135 59 60 71 72
-136 123 124 7 8
-137 121 128 52 53
-138 57 116 117 64
-139 58 59 118 119
-140 55 122 123 54
-141 35 68 124 27
-142 99 91 4 60
-143 105 106 53 54
-144 117 41 118 42
-145 13 14 81 82
-146 77 78 17 18
-147 35 36 95 96
-148 99 100 31 32
-149 89 90 37 38
-150 101 25 102 26
-151 77 1 8 76
-152 12 13 72 65
-153 85 9 86 10
-154 22 73 74 21
-155 16 105 8 97
-156 33 80 72 41
-157 100 3 59 92
-158 67 123 36 28
-159 34 67 42 75
-160 11 3 106 98
-161 89 2 58 97
-162 33 66 122 25
-163 1 2 125 126
-164 66 61 62 65
-165 48 40 73 65
-166 1 112 104 9
-167 3 4 127 128
-168 67 68 63 64
-169 78 2 79 3
-170 66 67 14 15
-171 39 72 128 31
-172 103 95 8 64
-173 23 24 75 76
-174 11 88 12 87
-175 103 27 104 28
-176 91 92 39 40
-177 110 13 118 21
-178 77 46 85 54
-179 111 24 16 119
-180 55 88 47 80
-181 121 122 5 6
-182 57 58 69 70
-183 22 23 90 91
-184 26 27 86 87
-185 71 127 40 32
-186 104 7 63 96
-187 51 84 43 76
-188 12 115 107 20
-189 38 39 106 107
-190 102 103 42 43
-191 123 26 115 18
-192 90 59 82 51
-193 22 14 117 109
-194 45 78 53 86
-195 29 30 97 98
-196 33 34 93 94
-197 6 7 74 75
-198 11 70 71 10
-199 88 57 49 96
-200 121 24 113 32
-201 49 82 41 74
-202 113 105 18 10
-203 62 95 54 87
-204 23 126 118 31
-205 121 34 26 65
-206 1 57 90 98
-207 58 91 50 83
-208 122 114 27 19
-209 100 13 5 108
-210 44 77 36 69
-211 44 119 43 120
-212 55 56 107 108
-213 25 17 128 120
-214 56 89 81 64
-215 55 94 63 86
-216 22 127 30 119
-217 111 14 103 6
-218 78 47 70 39
-219 110 34 111 35
-220 99 46 47 98
-221 11 116 19 108
-222 44 83 52 75
-223 102 5 61 94
-224 69 125 38 30
-225 94 18 95 19
-226 82 83 30 31
-227 100 101 48 41
-228 112 36 37 105
-229 99 2 107 10
-230 66 35 74 43
-231 110 102 15 7
-232 46 79 38 71
-233 23 112 15 120
-234 56 79 48 87
-235 44 45 104 97
-236 33 40 108 109
-237 15 16 83 84
-238 79 80 19 20
-239 24 92 93 17
-240 88 81 28 29
-241 113 60 61 120
-242 56 124 125 49
-243 111 112 51 52
-244 47 48 115 116
-245 12 101 4 109
-246 45 68 37 76
-247 25 84 85 32
-248 89 96 20 21
-249 80 4 5 73
-250 68 69 16 9
-251 101 93 6 62
-252 37 70 126 29
-253 60 93 52 85
-254 124 116 29 21
-255 125 28 117 20
-256 92 61 84 53
0