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