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