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