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