Graph forms
for C4 [ 256, 32 ] = KE_64(1,31,2,35,1)
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On this page are computer-accessible forms for the graph C4[ 256, 32 ] =
KE_64(1,31,2,35,1).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {2, 3}, {254, 255}, {252, 253}, {250, 251}, {248, 249}, {246,
247}, {244, 245}, {242, 243}, {240, 241}, {238, 239}, {236, 237}, {234, 235},
{232, 233}, {230, 231}, {228, 229}, {226, 227}, {224, 225}, {222, 223}, {220,
221}, {218, 219}, {216, 217}, {214, 215}, {212, 213}, {210, 211}, {208, 209},
{206, 207}, {204, 205}, {202, 203}, {200, 201}, {198, 199}, {196, 197}, {194,
195}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {4,
5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21},
{22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {34, 35}, {36, 37},
{38, 39}, {40, 41}, {42, 43}, {44, 45}, {46, 47}, {48, 49}, {128, 130}, {1, 2},
{253, 254}, {249, 250}, {245, 246}, {241, 242}, {237, 238}, {233, 234}, {229,
230}, {225, 226}, {221, 222}, {217, 218}, {213, 214}, {209, 210}, {205, 206},
{201, 202}, {197, 198}, {193, 194}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {5,
6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37,
38}, {41, 42}, {45, 46}, {3, 4}, {251, 252}, {243, 244}, {235, 236}, {227, 228},
{219, 220}, {211, 212}, {203, 204}, {195, 196}, {59, 60}, {51, 52}, {11, 12},
{19, 20}, {27, 28}, {35, 36}, {43, 44}, {7, 8}, {247, 248}, {231, 232}, {215,
216}, {199, 200}, {55, 56}, {23, 24}, {39, 40}, {15, 16}, {239, 240}, {207,
208}, {47, 48}, {64, 97}, {31, 32}, {223, 224}, {128, 192}, {191, 255}, {190,
254}, {189, 253}, {188, 252}, {187, 251}, {186, 250}, {129, 193}, {130, 194},
{131, 195}, {132, 196}, {133, 197}, {134, 198}, {135, 199}, {136, 200}, {137,
201}, {138, 202}, {139, 203}, {140, 204}, {141, 205}, {142, 206}, {143, 207},
{144, 208}, {145, 209}, {146, 210}, {147, 211}, {148, 212}, {149, 213}, {150,
214}, {151, 215}, {152, 216}, {153, 217}, {154, 218}, {155, 219}, {156, 220},
{157, 221}, {158, 222}, {159, 223}, {160, 224}, {161, 225}, {162, 226}, {163,
227}, {164, 228}, {165, 229}, {166, 230}, {167, 231}, {168, 232}, {169, 233},
{170, 234}, {171, 235}, {172, 236}, {173, 237}, {174, 238}, {175, 239}, {176,
240}, {177, 241}, {178, 242}, {179, 243}, {180, 244}, {181, 245}, {182, 246},
{183, 247}, {184, 248}, {185, 249}, {1, 64}, {63, 96}, {2, 99}, {62, 95}, {60,
93}, {58, 91}, {56, 89}, {54, 87}, {52, 85}, {50, 83}, {4, 101}, {6, 103}, {8,
105}, {10, 107}, {12, 109}, {14, 111}, {16, 113}, {18, 115}, {20, 117}, {22,
119}, {24, 121}, {26, 123}, {28, 125}, {30, 127}, {32, 65}, {34, 67}, {36, 69},
{38, 71}, {40, 73}, {42, 75}, {44, 77}, {46, 79}, {48, 81}, {1, 98}, {61, 94},
{57, 90}, {53, 86}, {49, 82}, {5, 102}, {9, 106}, {13, 110}, {17, 114}, {21,
118}, {25, 122}, {29, 126}, {33, 66}, {37, 70}, {41, 74}, {45, 78}, {128, 227},
{3, 100}, {59, 92}, {51, 84}, {11, 108}, {19, 116}, {27, 124}, {35, 68}, {43,
76}, {7, 104}, {55, 88}, {23, 120}, {39, 72}, {15, 112}, {63, 64}, {47, 80}, {1,
129}, {64, 192}, {63, 191}, {62, 190}, {61, 189}, {60, 188}, {59, 187}, {58,
186}, {57, 185}, {56, 184}, {55, 183}, {54, 182}, {53, 181}, {52, 180}, {51,
179}, {50, 178}, {49, 177}, {48, 176}, {2, 130}, {3, 131}, {4, 132}, {5, 133},
{6, 134}, {7, 135}, {8, 136}, {9, 137}, {10, 138}, {11, 139}, {12, 140}, {13,
141}, {14, 142}, {15, 143}, {16, 144}, {17, 145}, {18, 146}, {19, 147}, {20,
148}, {21, 149}, {22, 150}, {23, 151}, {24, 152}, {25, 153}, {26, 154}, {27,
155}, {28, 156}, {29, 157}, {30, 158}, {31, 159}, {32, 160}, {33, 161}, {34,
162}, {35, 163}, {36, 164}, {37, 165}, {38, 166}, {39, 167}, {40, 168}, {41,
169}, {42, 170}, {43, 171}, {44, 172}, {45, 173}, {46, 174}, {47, 175}, {95,
194}, {125, 224}, {127, 226}, {31, 128}, {94, 193}, {126, 225}, {68, 231}, {84,
247}, {80, 243}, {76, 239}, {72, 235}, {88, 251}, {92, 255}, {96, 195}, {100,
199}, {104, 203}, {108, 207}, {112, 211}, {116, 215}, {120, 219}, {124, 223},
{65, 228}, {83, 246}, {81, 244}, {75, 238}, {73, 236}, {67, 230}, {89, 252},
{91, 254}, {97, 196}, {99, 198}, {105, 204}, {107, 206}, {113, 212}, {115, 214},
{121, 220}, {123, 222}, {66, 229}, {82, 245}, {74, 237}, {90, 253}, {98, 197},
{106, 205}, {114, 213}, {122, 221}, {69, 232}, {85, 248}, {71, 234}, {87, 250},
{101, 200}, {103, 202}, {117, 216}, {119, 218}, {70, 233}, {86, 249}, {102,
201}, {118, 217}, {77, 240}, {79, 242}, {109, 208}, {111, 210}, {126, 192}, {78,
241}, {110, 209}, {65, 129}, {86, 150}, {85, 149}, {84, 148}, {83, 147}, {82,
146}, {81, 145}, {80, 144}, {79, 143}, {78, 142}, {77, 141}, {76, 140}, {75,
139}, {74, 138}, {73, 137}, {72, 136}, {71, 135}, {70, 134}, {69, 133}, {68,
132}, {67, 131}, {66, 130}, {87, 151}, {88, 152}, {89, 153}, {90, 154}, {91,
155}, {92, 156}, {93, 157}, {94, 158}, {95, 159}, {96, 160}, {97, 161}, {98,
162}, {99, 163}, {100, 164}, {101, 165}, {102, 166}, {103, 167}, {104, 168},
{105, 169}, {106, 170}, {107, 171}, {108, 172}, {109, 173}, {110, 174}, {111,
175}, {112, 176}, {113, 177}, {114, 178}, {115, 179}, {116, 180}, {117, 181},
{118, 182}, {119, 183}, {120, 184}, {121, 185}, {122, 186}, {123, 187}, {124,
188}, {125, 189}, {126, 190}, {127, 191}, {65, 131}, {85, 151}, {84, 150}, {81,
147}, {80, 146}, {77, 143}, {76, 142}, {73, 139}, {72, 138}, {69, 135}, {68,
134}, {88, 154}, {89, 155}, {92, 158}, {93, 159}, {96, 162}, {97, 163}, {100,
166}, {101, 167}, {104, 170}, {105, 171}, {108, 174}, {109, 175}, {112, 178},
{113, 179}, {116, 182}, {117, 183}, {120, 186}, {121, 187}, {124, 190}, {125,
191}, {66, 132}, {83, 149}, {82, 148}, {75, 141}, {74, 140}, {67, 133}, {90,
156}, {91, 157}, {98, 164}, {99, 165}, {106, 172}, {107, 173}, {114, 180}, {115,
181}, {122, 188}, {123, 189}, {70, 136}, {86, 152}, {71, 137}, {87, 153}, {102,
168}, {103, 169}, {118, 184}, {119, 185}, {78, 144}, {79, 145}, {110, 176},
{111, 177}, {94, 160}, {95, 161}, {127, 129}, {93, 256}, {192, 256}, {193, 256},
{255, 256} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
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,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64)(65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128)(129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180,
181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192)(193, 194, 195, 196,
197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228,
229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256) (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, 64)(3, 63)(4, 62)(5, 61)(6, 60)(7, 59)(8, 58)(9, 57)(10, 56)(11, 55)(12,
54)(13, 53)(14, 52)(15, 51)(16, 50)(17, 49)(18, 48)(19, 47)(20, 46)(21, 45)(22,
44)(23, 43)(24, 42)(25, 41)(26, 40)(27, 39)(28, 38)(29, 37)(30, 36)(31, 35)(32,
34)(65, 162)(66, 161)(67, 160)(68, 159)(69, 158)(70, 157)(71, 156)(72, 155)(73,
154)(74, 153)(75, 152)(76, 151)(77, 150)(78, 149)(79, 148)(80, 147)(81, 146)(82,
145)(83, 144)(84, 143)(85, 142)(86, 141)(87, 140)(88, 139)(89, 138)(90, 137)(91,
136)(92, 135)(93, 134)(94, 133)(95, 132)(96, 131)(97, 130)(98, 129)(99,
192)(100, 191)(101, 190)(102, 189)(103, 188)(104, 187)(105, 186)(106, 185)(107,
184)(108, 183)(109, 182)(110, 181)(111, 180)(112, 179)(113, 178)(114, 177)(115,
176)(116, 175)(117, 174)(118, 173)(119, 172)(120, 171)(121, 170)(122, 169)(123,
168)(124, 167)(125, 166)(126, 165)(127, 164)(128, 163)(193, 197)(194, 196)(198,
256)(199, 255)(200, 254)(201, 253)(202, 252)(203, 251)(204, 250)(205, 249)(206,
248)(207, 247)(208, 246)(209, 245)(210, 244)(211, 243)(212, 242)(213, 241)(214,
240)(215, 239)(216, 238)(217, 237)(218, 236)(219, 235)(220, 234)(221, 233)(222,
232)(223, 231)(224, 230)(225, 229)(226, 228)
c: (2, 98)(3, 164)(4, 36)(5, 37)(6, 70)(7, 136)(10, 106)(11, 172)(12, 44)(13,
45)(14, 78)(15, 144)(18, 114)(19, 180)(20, 52)(21, 53)(22, 86)(23, 152)(26,
122)(27, 188)(28, 60)(29, 61)(30, 94)(31, 160)(34, 66)(35, 132)(38, 102)(39,
168)(42, 74)(43, 140)(46, 110)(47, 176)(50, 82)(51, 148)(54, 118)(55, 184)(58,
90)(59, 156)(62, 126)(63, 192)(67, 229)(69, 101)(71, 201)(72, 104)(75, 237)(77,
109)(79, 209)(80, 112)(83, 245)(85, 117)(87, 217)(88, 120)(91, 253)(93, 125)(95,
225)(96, 128)(99, 197)(103, 233)(107, 205)(111, 241)(115, 213)(119, 249)(123,
221)(127, 193)(130, 162)(131, 228)(133, 165)(135, 200)(138, 170)(139, 236)(141,
173)(143, 208)(146, 178)(147, 244)(149, 181)(151, 216)(154, 186)(155, 252)(157,
189)(159, 224)(163, 196)(167, 232)(171, 204)(175, 240)(179, 212)(183, 248)(187,
220)(191, 256)(194, 226)(195, 227)(202, 234)(203, 235)(210, 242)(211, 243)(218,
250)(219, 251)
C4[ 256, 32 ]
256
-1 2 129 64 98
-2 99 1 3 130
-3 100 2 4 131
-4 132 101 3 5
-5 133 102 4 6
-6 134 103 5 7
-7 135 104 6 8
-8 136 105 7 9
-9 137 106 8 10
-10 11 138 107 9
-11 12 139 108 10
-12 11 13 140 109
-13 110 12 14 141
-14 111 13 15 142
-15 143 112 14 16
-16 144 113 15 17
-17 145 114 16 18
-18 146 115 17 19
-19 147 116 18 20
-20 148 117 19 21
-21 22 149 118 20
-22 23 150 119 21
-23 22 24 151 120
-24 121 23 25 152
-25 122 24 26 153
-26 154 123 25 27
-27 155 124 26 28
-28 156 125 27 29
-29 157 126 28 30
-30 158 127 29 31
-31 159 128 30 32
-32 33 160 31 65
-33 66 34 161 32
-34 33 67 35 162
-35 34 68 36 163
-36 35 69 37 164
-37 165 36 70 38
-38 166 37 71 39
-39 167 38 72 40
-40 168 39 73 41
-41 169 40 74 42
-42 170 41 75 43
-43 44 171 42 76
-44 77 45 172 43
-45 44 78 46 173
-46 45 79 47 174
-47 46 80 48 175
-48 176 47 81 49
-49 177 48 82 50
-50 178 49 83 51
-51 179 50 84 52
-52 180 51 85 53
-53 181 52 86 54
-54 55 182 53 87
-55 88 56 183 54
-56 55 89 57 184
-57 56 90 58 185
-58 57 91 59 186
-59 187 58 92 60
-60 188 59 93 61
-61 189 60 94 62
-62 190 61 95 63
-63 191 62 96 64
-64 1 192 63 97
-65 129 228 32 131
-66 33 132 130 229
-67 34 133 131 230
-68 132 231 35 134
-69 133 232 36 135
-70 134 233 37 136
-71 135 234 38 137
-72 136 235 39 138
-73 137 236 40 139
-74 138 237 41 140
-75 139 238 42 141
-76 140 239 43 142
-77 44 143 141 240
-78 45 144 142 241
-79 143 242 46 145
-80 144 243 47 146
-81 145 244 48 147
-82 146 245 49 148
-83 147 246 50 149
-84 148 247 51 150
-85 149 248 52 151
-86 150 249 53 152
-87 151 250 54 153
-88 55 154 152 251
-89 56 155 153 252
-90 154 253 57 156
-91 155 254 58 157
-92 156 255 59 158
-93 157 256 60 159
-94 158 61 160 193
-95 159 62 161 194
-96 160 63 162 195
-97 161 64 163 196
-98 1 162 164 197
-99 165 198 2 163
-100 166 199 3 164
-101 165 167 200 4
-102 166 168 201 5
-103 167 169 202 6
-104 168 170 203 7
-105 169 171 204 8
-106 170 172 205 9
-107 171 173 206 10
-108 11 172 174 207
-109 12 173 175 208
-110 176 209 13 174
-111 177 210 14 175
-112 176 178 211 15
-113 177 179 212 16
-114 178 180 213 17
-115 179 181 214 18
-116 180 182 215 19
-117 181 183 216 20
-118 182 184 217 21
-119 22 183 185 218
-120 23 184 186 219
-121 187 220 24 185
-122 188 221 25 186
-123 187 189 222 26
-124 188 190 223 27
-125 189 191 224 28
-126 190 192 225 29
-127 191 226 30 129
-128 192 227 31 130
-129 1 127 193 65
-130 66 2 128 194
-131 67 3 195 65
-132 66 68 4 196
-133 67 69 5 197
-134 198 68 70 6
-135 199 69 71 7
-136 200 70 72 8
-137 201 71 73 9
-138 202 72 74 10
-139 11 203 73 75
-140 12 204 74 76
-141 77 13 205 75
-142 78 14 206 76
-143 77 79 15 207
-144 78 80 16 208
-145 209 79 81 17
-146 210 80 82 18
-147 211 81 83 19
-148 212 82 84 20
-149 213 83 85 21
-150 22 214 84 86
-151 23 215 85 87
-152 88 24 216 86
-153 89 25 217 87
-154 88 90 26 218
-155 89 91 27 219
-156 220 90 92 28
-157 221 91 93 29
-158 222 92 94 30
-159 223 93 95 31
-160 224 94 96 32
-161 33 225 95 97
-162 34 226 96 98
-163 99 35 227 97
-164 100 36 228 98
-165 99 101 37 229
-166 100 102 38 230
-167 231 101 103 39
-168 232 102 104 40
-169 233 103 105 41
-170 234 104 106 42
-171 235 105 107 43
-172 44 236 106 108
-173 45 237 107 109
-174 110 46 238 108
-175 111 47 239 109
-176 110 112 48 240
-177 111 113 49 241
-178 242 112 114 50
-179 243 113 115 51
-180 244 114 116 52
-181 245 115 117 53
-182 246 116 118 54
-183 55 247 117 119
-184 56 248 118 120
-185 121 57 249 119
-186 122 58 250 120
-187 121 123 59 251
-188 122 124 60 252
-189 253 123 125 61
-190 254 124 126 62
-191 255 125 127 63
-192 256 126 128 64
-193 256 94 194 129
-194 193 95 195 130
-195 194 96 196 131
-196 132 195 97 197
-197 198 133 196 98
-198 99 199 134 197
-199 198 100 200 135
-200 199 101 201 136
-201 200 102 202 137
-202 201 103 203 138
-203 202 104 204 139
-204 203 105 205 140
-205 204 106 206 141
-206 205 107 207 142
-207 143 206 108 208
-208 209 144 207 109
-209 110 210 145 208
-210 209 111 211 146
-211 210 112 212 147
-212 211 113 213 148
-213 212 114 214 149
-214 213 115 215 150
-215 214 116 216 151
-216 215 117 217 152
-217 216 118 218 153
-218 154 217 119 219
-219 220 155 218 120
-220 121 221 156 219
-221 220 122 222 157
-222 221 123 223 158
-223 222 124 224 159
-224 223 125 225 160
-225 224 126 226 161
-226 225 127 227 162
-227 226 128 228 163
-228 227 229 65 164
-229 66 165 228 230
-230 231 67 166 229
-231 232 68 167 230
-232 231 233 69 168
-233 232 234 70 169
-234 233 235 71 170
-235 234 236 72 171
-236 235 237 73 172
-237 236 238 74 173
-238 237 239 75 174
-239 238 240 76 175
-240 77 176 239 241
-241 242 78 177 240
-242 243 79 178 241
-243 242 244 80 179
-244 243 245 81 180
-245 244 246 82 181
-246 245 247 83 182
-247 246 248 84 183
-248 247 249 85 184
-249 248 250 86 185
-250 249 251 87 186
-251 88 187 250 252
-252 253 89 188 251
-253 254 90 189 252
-254 253 255 91 190
-255 254 256 92 191
-256 255 93 192 193
0