Graph forms
for C4 [ 258, 3 ] = PS(6,43;6)
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On this page are computer-accessible forms for the graph C4[ 258, 3 ] =
PS(6,43;6).
(I) Following is a form readable by MAGMA:
g:=Graph<258|{ {172, 173}, {81, 87}, {43, 44}, {128, 135}, {129, 136}, {82, 88},
{215, 221}, {214, 220}, {211, 217}, {210, 216}, {86, 92}, {83, 89}, {84, 90},
{213, 219}, {212, 218}, {85, 91}, {128, 164}, {129, 165}, {64, 101}, {210, 247},
{208, 245}, {82, 119}, {80, 117}, {74, 111}, {72, 109}, {66, 103}, {192, 229},
{194, 231}, {200, 237}, {202, 239}, {65, 102}, {209, 246}, {81, 118}, {73, 110},
{193, 230}, {201, 238}, {4, 46}, {5, 47}, {16, 58}, {17, 59}, {20, 62}, {21,
63}, {132, 174}, {133, 175}, {144, 186}, {145, 187}, {148, 190}, {149, 191},
{67, 104}, {215, 252}, {211, 248}, {83, 120}, {71, 108}, {195, 232}, {199, 236},
{1, 45}, {2, 46}, {3, 47}, {16, 60}, {17, 61}, {18, 62}, {19, 63}, {130, 174},
{131, 175}, {144, 188}, {145, 189}, {146, 190}, {147, 191}, {68, 105}, {214,
251}, {212, 249}, {86, 123}, {84, 121}, {70, 107}, {196, 233}, {198, 235}, {2,
44}, {3, 45}, {18, 60}, {19, 61}, {131, 173}, {146, 188}, {147, 189}, {69, 106},
{213, 250}, {85, 122}, {197, 234}, {64, 113}, {206, 255}, {78, 127}, {76, 125},
{74, 123}, {72, 121}, {70, 119}, {68, 117}, {66, 115}, {192, 241}, {194, 243},
{196, 245}, {198, 247}, {200, 249}, {202, 251}, {204, 253}, {65, 114}, {205,
254}, {77, 126}, {73, 122}, {69, 118}, {193, 242}, {197, 246}, {201, 250}, {4,
48}, {5, 49}, {6, 50}, {7, 51}, {12, 56}, {13, 57}, {14, 58}, {15, 59}, {132,
176}, {133, 177}, {134, 178}, {135, 179}, {140, 184}, {141, 185}, {142, 186},
{143, 187}, {6, 48}, {7, 49}, {14, 56}, {15, 57}, {134, 176}, {135, 177}, {142,
184}, {143, 185}, {67, 116}, {75, 124}, {195, 244}, {203, 252}, {8, 50}, {9,
51}, {12, 54}, {13, 55}, {136, 178}, {137, 179}, {140, 182}, {141, 183}, {75,
112}, {207, 244}, {79, 116}, {203, 240}, {8, 52}, {9, 53}, {10, 54}, {11, 55},
{136, 180}, {137, 181}, {138, 182}, {139, 183}, {76, 113}, {206, 243}, {78,
115}, {204, 241}, {10, 52}, {11, 53}, {138, 180}, {139, 181}, {71, 120}, {205,
242}, {77, 114}, {199, 248}, {47, 96}, {63, 112}, {175, 224}, {191, 240}, {44,
124}, {47, 127}, {46, 126}, {45, 125}, {173, 253}, {174, 254}, {175, 255}, {48,
97}, {62, 111}, {60, 109}, {58, 107}, {56, 105}, {54, 103}, {52, 101}, {50, 99},
{176, 225}, {178, 227}, {180, 229}, {182, 231}, {184, 233}, {186, 235}, {188,
237}, {190, 239}, {49, 98}, {61, 110}, {57, 106}, {53, 102}, {177, 226}, {181,
230}, {185, 234}, {189, 238}, {20, 64}, {21, 65}, {22, 66}, {23, 67}, {28, 72},
{29, 73}, {30, 74}, {31, 75}, {148, 192}, {149, 193}, {150, 194}, {151, 195},
{156, 200}, {157, 201}, {158, 202}, {159, 203}, {130, 215}, {22, 64}, {23, 65},
{30, 72}, {31, 73}, {150, 192}, {151, 193}, {158, 200}, {159, 201}, {1, 86},
{59, 108}, {51, 100}, {179, 228}, {187, 236}, {24, 66}, {25, 67}, {28, 70}, {29,
71}, {152, 194}, {153, 195}, {156, 198}, {157, 199}, {59, 96}, {63, 100}, {187,
224}, {191, 228}, {24, 68}, {25, 69}, {26, 70}, {27, 71}, {152, 196}, {153,
197}, {154, 198}, {155, 199}, {60, 97}, {62, 99}, {188, 225}, {190, 227}, {26,
68}, {27, 69}, {154, 196}, {155, 197}, {55, 104}, {61, 98}, {183, 232}, {189,
226}, {50, 87}, {58, 95}, {56, 93}, {184, 221}, {186, 223}, {57, 94}, {185,
222}, {32, 74}, {33, 75}, {36, 78}, {37, 79}, {160, 202}, {161, 203}, {164,
206}, {165, 207}, {51, 88}, {55, 92}, {179, 216}, {183, 220}, {32, 76}, {33,
77}, {34, 78}, {35, 79}, {160, 204}, {161, 205}, {162, 206}, {163, 207}, {52,
89}, {54, 91}, {180, 217}, {182, 219}, {34, 76}, {35, 77}, {162, 204}, {163,
205}, {53, 90}, {181, 218}, {44, 93}, {46, 95}, {174, 223}, {45, 94}, {173,
222}, {36, 80}, {37, 81}, {38, 82}, {39, 83}, {164, 208}, {165, 209}, {166,
210}, {167, 211}, {38, 80}, {39, 81}, {166, 208}, {167, 209}, {40, 82}, {41,
83}, {168, 210}, {169, 211}, {172, 214}, {40, 84}, {41, 85}, {42, 86}, {168,
212}, {169, 213}, {170, 214}, {171, 215}, {42, 84}, {43, 85}, {170, 212}, {171,
213}, {48, 128}, {49, 129}, {94, 144}, {111, 161}, {110, 160}, {95, 145}, {79,
128}, {8, 216}, {43, 251}, {9, 217}, {10, 218}, {11, 219}, {12, 220}, {13, 221},
{14, 222}, {15, 223}, {32, 240}, {33, 241}, {34, 242}, {35, 243}, {36, 244},
{37, 245}, {38, 246}, {39, 247}, {40, 248}, {41, 249}, {42, 250}, {80, 129},
{88, 138}, {112, 162}, {93, 143}, {92, 142}, {89, 139}, {113, 163}, {116, 166},
{117, 167}, {120, 170}, {121, 171}, {90, 140}, {91, 141}, {114, 164}, {115,
165}, {122, 172}, {94, 130}, {95, 131}, {124, 160}, {125, 161}, {126, 162},
{127, 163}, {1, 223}, {87, 137}, {32, 254}, {33, 255}, {118, 168}, {119, 169},
{2, 224}, {3, 225}, {6, 228}, {7, 229}, {10, 232}, {11, 233}, {14, 236}, {15,
237}, {18, 240}, {19, 241}, {22, 244}, {23, 245}, {26, 248}, {27, 249}, {30,
252}, {31, 253}, {96, 132}, {113, 149}, {112, 148}, {107, 143}, {106, 142},
{105, 141}, {104, 140}, {99, 135}, {98, 134}, {97, 133}, {114, 150}, {115, 151},
{120, 156}, {121, 157}, {122, 158}, {123, 159}, {4, 226}, {5, 227}, {12, 234},
{13, 235}, {20, 242}, {21, 243}, {28, 250}, {29, 251}, {100, 136}, {103, 139},
{102, 138}, {101, 137}, {116, 152}, {117, 153}, {118, 154}, {119, 155}, {8,
230}, {9, 231}, {24, 246}, {25, 247}, {16, 224}, {17, 225}, {18, 226}, {19,
227}, {20, 228}, {21, 229}, {22, 230}, {23, 231}, {24, 232}, {25, 233}, {26,
234}, {27, 235}, {28, 236}, {29, 237}, {30, 238}, {31, 239}, {87, 166}, {93,
172}, {91, 170}, {89, 168}, {96, 146}, {109, 159}, {108, 158}, {105, 155}, {104,
154}, {101, 151}, {100, 150}, {97, 147}, {40, 219}, {90, 169}, {41, 220}, {43,
222}, {98, 148}, {107, 157}, {106, 156}, {99, 149}, {42, 221}, {92, 171}, {123,
130}, {125, 132}, {127, 134}, {4, 255}, {126, 133}, {108, 144}, {111, 147},
{110, 146}, {109, 145}, {1, 252}, {3, 254}, {37, 216}, {39, 218}, {16, 238},
{103, 153}, {102, 152}, {17, 239}, {2, 253}, {88, 167}, {38, 217}, {124, 131},
{5, 256}, {7, 258}, {6, 257}, {34, 256}, {35, 257}, {36, 258}, {176, 256}, {177,
257}, {178, 258}, {207, 256}, {208, 257}, {209, 258} }>;
(II) A more general form is to represent the graph as the orbit of {172, 173}
under the group generated by the following permutations:
a: (1, 44, 87, 130, 173, 216)(2, 50, 123, 131, 179, 252)(3, 56, 116, 132, 185,
245)(4, 62, 109, 133, 191, 238)(5, 68, 102, 134, 197, 231)(6, 74, 95, 135, 203,
224)(7, 80, 88, 136, 209, 217)(8, 86, 124, 137, 215, 253)(9, 49, 117, 138, 178,
246)(10, 55, 110, 139, 184, 239)(11, 61, 103, 140, 190, 232)(12, 67, 96, 141,
196, 225)(13, 73, 89, 142, 202, 218)(14, 79, 125, 143, 208, 254)(15, 85, 118,
144, 214, 247)(16, 48, 111, 145, 177, 240)(17, 54, 104, 146, 183, 233)(18, 60,
97, 147, 189, 226)(19, 66, 90, 148, 195, 219)(20, 72, 126, 149, 201, 255)(21,
78, 119, 150, 207, 248)(22, 84, 112, 151, 213, 241)(23, 47, 105, 152, 176,
234)(24, 53, 98, 153, 182, 227)(25, 59, 91, 154, 188, 220)(26, 65, 127, 155,
194, 256)(27, 71, 120, 156, 200, 249)(28, 77, 113, 157, 206, 242)(29, 83, 106,
158, 212, 235)(30, 46, 99, 159, 175, 228)(31, 52, 92, 160, 181, 221)(32, 58,
128, 161, 187, 257)(33, 64, 121, 162, 193, 250)(34, 70, 114, 163, 199, 243)(35,
76, 107, 164, 205, 236)(36, 82, 100, 165, 211, 229)(37, 45, 93, 166, 174,
222)(38, 51, 129, 167, 180, 258)(39, 57, 122, 168, 186, 251)(40, 63, 115, 169,
192, 244)(41, 69, 108, 170, 198, 237)(42, 75, 101, 171, 204, 230)(43, 81, 94,
172, 210, 223) (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: (2, 43)(3, 42)(4, 41)(5, 40)(6, 39)(7, 38)(8, 37)(9, 36)(10, 35)(11, 34)(12,
33)(13, 32)(14, 31)(15, 30)(16, 29)(17, 28)(18, 27)(19, 26)(20, 25)(21, 24)(22,
23)(45, 86)(46, 85)(47, 84)(48, 83)(49, 82)(50, 81)(51, 80)(52, 79)(53, 78)(54,
77)(55, 76)(56, 75)(57, 74)(58, 73)(59, 72)(60, 71)(61, 70)(62, 69)(63, 68)(64,
67)(65, 66)(88, 129)(89, 128)(90, 127)(91, 126)(92, 125)(93, 124)(94, 123)(95,
122)(96, 121)(97, 120)(98, 119)(99, 118)(100, 117)(101, 116)(102, 115)(103,
114)(104, 113)(105, 112)(106, 111)(107, 110)(108, 109)(131, 172)(132, 171)(133,
170)(134, 169)(135, 168)(136, 167)(137, 166)(138, 165)(139, 164)(140, 163)(141,
162)(142, 161)(143, 160)(144, 159)(145, 158)(146, 157)(147, 156)(148, 155)(149,
154)(150, 153)(151, 152)(174, 215)(175, 214)(176, 213)(177, 212)(178, 211)(179,
210)(180, 209)(181, 208)(182, 207)(183, 206)(184, 205)(185, 204)(186, 203)(187,
202)(188, 201)(189, 200)(190, 199)(191, 198)(192, 197)(193, 196)(194, 195)(217,
258)(218, 257)(219, 256)(220, 255)(221, 254)(222, 253)(223, 252)(224, 251)(225,
250)(226, 249)(227, 248)(228, 247)(229, 246)(230, 245)(231, 244)(232, 243)(233,
242)(234, 241)(235, 240)(236, 239)(237, 238)
c: (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, 257, 258)
C4[ 258, 3 ]
258
-1 45 223 86 252
-2 44 253 46 224
-3 45 254 47 225
-4 46 255 48 226
-5 47 256 49 227
-6 48 257 50 228
-7 49 258 51 229
-8 50 216 52 230
-9 231 51 217 53
-10 232 52 218 54
-11 55 233 53 219
-12 220 56 234 54
-13 55 221 57 235
-14 56 222 58 236
-15 57 223 59 237
-16 58 224 60 238
-17 59 225 61 239
-18 60 226 62 240
-19 61 227 63 241
-20 242 62 228 64
-21 243 63 229 65
-22 66 244 64 230
-23 231 67 245 65
-24 66 232 68 246
-25 67 233 69 247
-26 68 234 70 248
-27 69 235 71 249
-28 70 236 72 250
-29 71 237 73 251
-30 72 238 74 252
-31 253 73 239 75
-32 254 74 240 76
-33 77 255 75 241
-34 242 78 256 76
-35 77 243 79 257
-36 78 244 80 258
-37 79 245 81 216
-38 80 246 82 217
-39 81 247 83 218
-40 82 248 84 219
-41 220 83 249 85
-42 221 84 250 86
-43 44 222 85 251
-44 2 124 93 43
-45 1 3 125 94
-46 2 4 126 95
-47 3 5 127 96
-48 4 6 128 97
-49 5 7 129 98
-50 99 6 8 87
-51 88 100 7 9
-52 89 101 8 10
-53 11 90 102 9
-54 12 91 103 10
-55 11 13 92 104
-56 12 14 93 105
-57 13 15 94 106
-58 14 16 95 107
-59 15 17 96 108
-60 16 18 97 109
-61 110 17 19 98
-62 99 111 18 20
-63 100 112 19 21
-64 22 101 113 20
-65 23 102 114 21
-66 22 24 103 115
-67 23 25 104 116
-68 24 26 105 117
-69 25 27 106 118
-70 26 28 107 119
-71 27 29 108 120
-72 121 28 30 109
-73 110 122 29 31
-74 111 123 30 32
-75 33 112 124 31
-76 34 113 125 32
-77 33 35 114 126
-78 34 36 115 127
-79 35 37 116 128
-80 36 38 117 129
-81 37 39 118 87
-82 88 38 40 119
-83 89 39 41 120
-84 121 90 40 42
-85 122 91 41 43
-86 1 123 92 42
-87 166 81 137 50
-88 167 82 138 51
-89 168 83 139 52
-90 169 84 140 53
-91 170 85 141 54
-92 55 171 86 142
-93 44 143 56 172
-94 45 144 57 130
-95 46 145 58 131
-96 132 47 146 59
-97 133 48 147 60
-98 134 49 148 61
-99 135 50 149 62
-100 136 51 150 63
-101 137 52 151 64
-102 138 53 152 65
-103 66 139 54 153
-104 55 154 67 140
-105 56 155 68 141
-106 57 156 69 142
-107 143 58 157 70
-108 144 59 158 71
-109 145 60 159 72
-110 146 61 160 73
-111 147 62 161 74
-112 148 63 162 75
-113 149 64 163 76
-114 77 150 65 164
-115 66 165 78 151
-116 67 166 79 152
-117 68 167 80 153
-118 154 69 168 81
-119 155 70 169 82
-120 156 71 170 83
-121 157 72 171 84
-122 158 73 172 85
-123 159 74 86 130
-124 44 160 75 131
-125 132 45 161 76
-126 77 133 46 162
-127 78 134 47 163
-128 79 135 48 164
-129 165 80 136 49
-130 123 94 215 174
-131 124 95 173 175
-132 176 125 96 174
-133 177 126 97 175
-134 176 178 127 98
-135 99 177 179 128
-136 100 178 180 129
-137 101 179 181 87
-138 88 102 180 182
-139 89 103 181 183
-140 90 104 182 184
-141 91 105 183 185
-142 92 106 184 186
-143 187 93 107 185
-144 188 94 108 186
-145 187 189 95 109
-146 110 188 190 96
-147 111 189 191 97
-148 112 190 192 98
-149 99 113 191 193
-150 100 114 192 194
-151 101 115 193 195
-152 102 116 194 196
-153 103 117 195 197
-154 198 104 118 196
-155 199 105 119 197
-156 198 200 106 120
-157 121 199 201 107
-158 122 200 202 108
-159 123 201 203 109
-160 110 124 202 204
-161 111 125 203 205
-162 112 126 204 206
-163 113 127 205 207
-164 114 128 206 208
-165 209 115 129 207
-166 210 116 87 208
-167 88 209 211 117
-168 89 210 212 118
-169 90 211 213 119
-170 91 212 214 120
-171 121 92 213 215
-172 122 93 214 173
-173 253 222 172 131
-174 132 254 223 130
-175 133 255 224 131
-176 132 134 256 225
-177 133 135 257 226
-178 134 136 258 227
-179 135 137 216 228
-180 136 138 217 229
-181 137 139 218 230
-182 231 138 140 219
-183 220 232 139 141
-184 221 233 140 142
-185 143 222 234 141
-186 144 223 235 142
-187 143 145 224 236
-188 144 146 225 237
-189 145 147 226 238
-190 146 148 227 239
-191 147 149 228 240
-192 148 150 229 241
-193 242 149 151 230
-194 231 243 150 152
-195 232 244 151 153
-196 154 233 245 152
-197 155 234 246 153
-198 154 156 235 247
-199 155 157 236 248
-200 156 158 237 249
-201 157 159 238 250
-202 158 160 239 251
-203 159 161 240 252
-204 253 160 162 241
-205 242 254 161 163
-206 243 255 162 164
-207 165 244 256 163
-208 166 245 257 164
-209 165 167 246 258
-210 166 168 247 216
-211 167 169 248 217
-212 168 170 249 218
-213 169 171 250 219
-214 220 170 172 251
-215 221 171 130 252
-216 210 179 37 8
-217 211 180 38 9
-218 212 181 39 10
-219 11 213 182 40
-220 12 214 183 41
-221 13 215 184 42
-222 14 173 185 43
-223 1 15 174 186
-224 187 2 16 175
-225 176 188 3 17
-226 177 189 4 18
-227 178 190 5 19
-228 179 191 6 20
-229 180 192 7 21
-230 22 181 193 8
-231 23 182 194 9
-232 24 183 195 10
-233 11 25 184 196
-234 12 26 185 197
-235 198 13 27 186
-236 187 199 14 28
-237 188 200 15 29
-238 189 201 16 30
-239 190 202 17 31
-240 191 203 18 32
-241 33 192 204 19
-242 34 193 205 20
-243 35 194 206 21
-244 22 36 195 207
-245 23 37 196 208
-246 209 24 38 197
-247 198 210 25 39
-248 199 211 26 40
-249 200 212 27 41
-250 201 213 28 42
-251 202 214 29 43
-252 1 203 215 30
-253 2 204 173 31
-254 3 205 174 32
-255 33 4 206 175
-256 176 34 5 207
-257 177 35 6 208
-258 209 178 36 7
0