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