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