Graph forms
for C4 [ 285, 6 ] = AT[285,4]
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On this page are computer-accessible forms for the graph C4[ 285, 6 ] =
AT[285,4].
(I) Following is a form readable by MAGMA:
g:=Graph<285|{ {116, 117}, {274, 275}, {270, 271}, {1, 3}, {273, 275}, {116,
118}, {1, 2}, {272, 275}, {141, 142}, {1, 5}, {226, 230}, {2, 6}, {1, 4}, {280,
285}, {2, 7}, {155, 158}, {250, 252}, {91, 92}, {259, 260}, {200, 207}, {186,
189}, {3, 11}, {4, 12}, {259, 266}, {2, 8}, {279, 285}, {167, 173}, {5, 15}, {4,
14}, {3, 9}, {194, 201}, {278, 285}, {83, 95}, {3, 13}, {261, 267}, {181, 187},
{4, 10}, {183, 184}, {212, 219}, {6, 22}, {166, 182}, {10, 26}, {9, 25}, {8,
24}, {7, 23}, {108, 125}, {264, 281}, {128, 145}, {6, 20}, {270, 284}, {237,
255}, {206, 220}, {12, 30}, {7, 21}, {8, 27}, {238, 253}, {224, 243}, {5, 17},
{271, 283}, {8, 28}, {7, 19}, {6, 16}, {11, 29}, {9, 31}, {108, 122}, {5, 18},
{257, 278}, {226, 245}, {66, 85}, {166, 190}, {198, 222}, {173, 180}, {259,
282}, {234, 243}, {135, 157}, {268, 278}, {257, 282}, {258, 281}, {260, 281},
{263, 282}, {111, 112}, {264, 279}, {149, 181}, {128, 161}, {129, 160}, {13,
47}, {17, 50}, {197, 230}, {195, 224}, {21, 54}, {134, 165}, {14, 42}, {217,
252}, {14, 40}, {222, 248}, {197, 227}, {18, 52}, {15, 41}, {16, 55}, {214,
241}, {20, 51}, {17, 57}, {196, 236}, {21, 61}, {139, 163}, {18, 59}, {130,
171}, {9, 35}, {219, 241}, {13, 39}, {12, 38}, {11, 33}, {10, 32}, {139, 161},
{149, 191}, {19, 56}, {19, 63}, {205, 225}, {142, 162}, {201, 228}, {10, 36},
{20, 58}, {16, 62}, {12, 34}, {11, 37}, {133, 171}, {153, 182}, {82, 99}, {15,
60}, {152, 172}, {151, 162}, {69, 115}, {71, 113}, {138, 178}, {206, 246}, {15,
53}, {72, 114}, {16, 43}, {211, 239}, {13, 48}, {19, 46}, {17, 44}, {195, 253},
{14, 49}, {18, 45}, {27, 90}, {28, 93}, {154, 219}, {34, 96}, {158, 220}, {31,
91}, {29, 88}, {24, 94}, {40, 110}, {33, 103}, {32, 102}, {30, 89}, {48, 119},
{49, 120}, {53, 124}, {51, 122}, {34, 104}, {189, 247}, {167, 237}, {39, 109},
{38, 108}, {37, 111}, {35, 105}, {130, 200}, {24, 83}, {54, 125}, {50, 121},
{156, 208}, {179, 255}, {26, 87}, {28, 82}, {170, 228}, {37, 107}, {36, 106},
{25, 86}, {187, 244}, {169, 230}, {52, 123}, {31, 80}, {170, 250}, {140, 221},
{167, 246}, {23, 69}, {172, 254}, {136, 218}, {27, 72}, {178, 225}, {20, 64},
{184, 236}, {169, 253}, {27, 79}, {23, 67}, {22, 66}, {21, 65}, {148, 192}, {28,
73}, {30, 75}, {38, 112}, {29, 74}, {41, 113}, {42, 114}, {145, 201}, {23, 78},
{47, 118}, {45, 116}, {22, 76}, {135, 221}, {22, 77}, {190, 229}, {169, 242},
{63, 100}, {46, 117}, {36, 127}, {137, 210}, {138, 209}, {24, 68}, {179, 239},
{54, 106}, {152, 196}, {26, 71}, {181, 232}, {35, 126}, {141, 211}, {174, 240},
{25, 70}, {44, 115}, {152, 199}, {140, 237}, {178, 211}, {54, 84}, {58, 89},
{56, 92}, {177, 213}, {166, 195}, {188, 217}, {153, 255}, {130, 234}, {146,
251}, {168, 193}, {135, 236}, {147, 248}, {188, 208}, {43, 70}, {168, 197},
{162, 207}, {153, 247}, {160, 206}, {144, 255}, {168, 199}, {32, 81}, {143,
254}, {160, 210}, {142, 253}, {164, 208}, {33, 84}, {186, 207}, {132, 241},
{133, 240}, {34, 85}, {25, 97}, {185, 193}, {175, 215}, {26, 98}, {131, 251},
{147, 235}, {128, 249}, {164, 221}, {146, 235}, {30, 100}, {176, 202}, {31,
101}, {134, 252}, {146, 232}, {129, 250}, {32, 92}, {149, 233}, {136, 245}, {29,
99}, {33, 95}, {137, 247}, {132, 251}, {190, 193}, {76, 204}, {78, 206}, {115,
243}, {67, 194}, {119, 245}, {82, 209}, {122, 249}, {44, 168}, {46, 170}, {45,
169}, {90, 222}, {113, 245}, {67, 198}, {117, 240}, {88, 222}, {97, 231}, {103,
225}, {112, 246}, {39, 160}, {115, 244}, {127, 248}, {69, 205}, {104, 224}, {40,
161}, {90, 211}, {102, 239}, {64, 202}, {65, 203}, {124, 246}, {125, 247}, {89,
210}, {101, 238}, {108, 231}, {43, 167}, {62, 178}, {61, 177}, {60, 176}, {94,
210}, {116, 248}, {86, 219}, {97, 236}, {122, 244}, {41, 166}, {79, 192}, {98,
237}, {68, 212}, {98, 242}, {80, 193}, {84, 197}, {82, 195}, {70, 213}, {85,
198}, {81, 194}, {79, 220}, {56, 172}, {78, 218}, {76, 216}, {59, 175}, {58,
174}, {57, 173}, {102, 243}, {107, 254}, {83, 196}, {87, 192}, {107, 252}, {59,
163}, {61, 165}, {60, 164}, {86, 207}, {105, 240}, {107, 242}, {109, 244}, {57,
162}, {68, 223}, {97, 250}, {98, 249}, {106, 241}, {55, 171}, {69, 217}, {126,
226}, {72, 214}, {73, 215}, {66, 221}, {79, 208}, {58, 154}, {35, 128}, {51,
151}, {123, 223}, {124, 216}, {36, 129}, {38, 131}, {40, 142}, {71, 225}, {70,
224}, {126, 216}, {37, 130}, {101, 205}, {119, 223}, {39, 141}, {73, 227}, {72,
226}, {52, 158}, {49, 155}, {47, 132}, {59, 144}, {55, 156}, {51, 158}, {60,
145}, {74, 228}, {75, 229}, {123, 213}, {42, 133}, {53, 154}, {50, 157}, {48,
159}, {101, 202}, {120, 215}, {121, 214}, {61, 141}, {110, 223}, {42, 153}, {63,
140}, {56, 139}, {53, 134}, {91, 232}, {93, 233}, {94, 234}, {95, 235}, {127,
202}, {49, 135}, {57, 143}, {47, 152}, {110, 217}, {43, 147}, {46, 150}, {45,
149}, {44, 148}, {105, 209}, {99, 218}, {109, 215}, {41, 146}, {50, 137}, {106,
209}, {48, 140}, {90, 231}, {52, 138}, {102, 216}, {55, 136}, {89, 230}, {92,
156}, {88, 154}, {93, 159}, {83, 144}, {96, 165}, {81, 151}, {95, 151}, {112,
185}, {113, 184}, {114, 187}, {118, 188}, {80, 155}, {118, 189}, {77, 129},
{117, 185}, {81, 159}, {94, 145}, {91, 137}, {88, 139}, {111, 183}, {85, 143},
{93, 134}, {87, 177}, {105, 143}, {96, 136}, {86, 191}, {120, 147}, {77, 163},
{100, 138}, {121, 150}, {84, 164}, {96, 144}, {74, 187}, {78, 191}, {76, 189},
{103, 150}, {64, 179}, {77, 190}, {73, 186}, {65, 180}, {80, 165}, {67, 182},
{62, 201}, {75, 188}, {66, 181}, {64, 183}, {63, 200}, {62, 199}, {87, 174},
{65, 184}, {68, 185}, {71, 186}, {74, 180}, {99, 157}, {104, 150}, {75, 180},
{100, 256}, {103, 257}, {110, 264}, {111, 265}, {121, 272}, {104, 258}, {109,
263}, {123, 273}, {124, 274}, {125, 270}, {120, 271}, {119, 270}, {127, 260},
{126, 259}, {114, 269}, {131, 261}, {132, 268}, {131, 266}, {133, 267}, {148,
262}, {148, 256}, {159, 267}, {155, 268}, {157, 266}, {156, 263}, {172, 269},
{191, 283}, {163, 261}, {175, 265}, {161, 262}, {179, 276}, {176, 280}, {182,
282}, {183, 262}, {171, 275}, {175, 279}, {174, 279}, {173, 278}, {177, 266},
{176, 269}, {170, 276}, {203, 267}, {212, 277}, {218, 280}, {205, 261}, {203,
258}, {194, 265}, {200, 260}, {204, 256}, {212, 263}, {204, 280}, {196, 274},
{198, 273}, {213, 269}, {204, 277}, {192, 284}, {199, 281}, {220, 258}, {203,
277}, {214, 265}, {232, 264}, {234, 268}, {242, 277}, {233, 257}, {249, 272},
{235, 256}, {233, 262}, {251, 276}, {254, 271}, {227, 273}, {238, 284}, {239,
283}, {229, 272}, {227, 276}, {228, 284}, {231, 285}, {238, 274}, {229, 283}
}>;
(II) A more general form is to represent the graph as the orbit of {116, 117}
under the group generated by the following permutations:
a: (1, 2)(3, 6)(4, 7)(5, 8)(9, 16)(10, 19)(11, 20)(12, 21)(13, 22)(14, 23)(15,
24)(17, 27)(18, 28)(25, 43)(26, 46)(29, 51)(30, 54)(31, 55)(32, 56)(33, 58)(34,
61)(35, 62)(36, 63)(37, 64)(38, 65)(39, 66)(40, 67)(41, 68)(42, 69)(44, 72)(45,
73)(47, 76)(48, 77)(49, 78)(50, 79)(52, 82)(53, 83)(57, 90)(59, 93)(60, 94)(71,
117)(74, 122)(75, 125)(80, 136)(81, 139)(84, 89)(85, 141)(86, 147)(87, 150)(88,
151)(91, 156)(95, 154)(96, 165)(97, 167)(98, 170)(99, 158)(100, 106)(101,
171)(102, 172)(103, 174)(104, 177)(105, 178)(107, 179)(108, 180)(109, 181)(110,
182)(111, 183)(112, 184)(113, 185)(114, 115)(116, 186)(118, 189)(119, 190)(120,
191)(121, 192)(123, 195)(124, 196)(126, 199)(127, 200)(128, 201)(129, 140)(130,
202)(131, 203)(132, 204)(133, 205)(134, 144)(135, 206)(137, 208)(138, 209)(142,
198)(143, 211)(146, 212)(148, 214)(149, 215)(152, 216)(153, 217)(155, 218)(157,
220)(159, 163)(160, 221)(161, 194)(162, 222)(164, 210)(166, 223)(168, 226)(169,
227)(173, 231)(175, 233)(176, 234)(187, 244)(188, 247)(193, 245)(197, 230)(207,
248)(213, 224)(219, 235)(225, 240)(228, 249)(229, 270)(232, 263)(236, 246)(237,
250)(238, 275)(239, 254)(241, 256)(242, 276)(243, 269)(251, 277)(252, 255)(253,
273)(257, 279)(258, 266)(259, 281)(261, 267)(262, 265)(264, 282)(268, 280)(271,
283)(272, 284)(278, 285) (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, 4)(6, 12)(7, 10)(8, 14)(9, 11)(15, 17)(16, 38)(19, 36)(20, 34)(21,
32)(22, 30)(23, 26)(24, 49)(25, 37)(27, 42)(28, 40)(29, 35)(31, 33)(39, 48)(41,
44)(43, 112)(46, 127)(50, 60)(51, 96)(52, 59)(53, 57)(54, 92)(55, 108)(56,
106)(58, 85)(61, 81)(62, 131)(63, 129)(64, 104)(65, 102)(66, 89)(67, 87)(68,
120)(69, 71)(70, 111)(72, 114)(73, 110)(74, 126)(75, 76)(77, 100)(78, 98)(79,
153)(80, 95)(82, 161)(83, 155)(84, 91)(86, 107)(88, 105)(90, 133)(93, 142)(94,
135)(97, 130)(99, 128)(101, 103)(109, 119)(113, 115)(117, 248)(121, 176)(122,
136)(123, 175)(124, 173)(125, 156)(132, 152)(134, 162)(137, 164)(138, 163)(139,
209)(140, 160)(141, 159)(143, 154)(144, 158)(145, 157)(146, 168)(147, 185)(148,
166)(149, 169)(150, 202)(151, 165)(167, 246)(170, 260)(171, 231)(172, 241)(174,
198)(177, 194)(178, 261)(179, 258)(180, 216)(181, 230)(182, 192)(183, 224)(184,
243)(186, 217)(187, 226)(188, 189)(190, 256)(191, 242)(193, 235)(195, 262)(196,
268)(197, 232)(199, 251)(200, 250)(201, 266)(203, 239)(204, 229)(205, 225)(206,
237)(207, 252)(208, 247)(210, 221)(211, 267)(212, 271)(213, 265)(214, 269)(215,
223)(218, 249)(219, 254)(220, 255)(222, 240)(227, 264)(228, 259)(233, 253)(234,
236)(238, 257)(244, 245)(263, 270)(272, 280)(273, 279)(274, 278)(275, 285)(276,
281)(277, 283)(282, 284)
c: (3, 5, 4)(6, 7, 8)(9, 17, 14)(10, 11, 18)(12, 13, 15)(16, 23, 27)(19, 28,
20)(21, 24, 22)(25, 44, 42)(26, 37, 45)(29, 52, 32)(30, 48, 53)(31, 50, 49)(33,
59, 36)(34, 39, 60)(35, 57, 40)(38, 47, 41)(43, 69, 72)(46, 73, 64)(51, 56,
82)(54, 83, 77)(55, 78, 79)(58, 63, 93)(61, 94, 66)(62, 67, 90)(65, 68, 76)(70,
115, 114)(71, 111, 116)(74, 123, 102)(75, 119, 124)(80, 137, 135)(81, 88,
138)(84, 144, 129)(85, 141, 145)(86, 148, 133)(87, 130, 149)(89, 140, 134)(91,
157, 155)(92, 99, 158)(95, 163, 106)(96, 160, 164)(97, 168, 153)(98, 107,
169)(100, 159, 154)(101, 121, 120)(103, 175, 127)(104, 109, 176)(105, 162,
161)(108, 152, 166)(110, 126, 173)(112, 118, 113)(117, 186, 183)(122, 172,
195)(125, 196, 190)(128, 143, 142)(131, 132, 146)(136, 206, 208)(139, 209,
151)(147, 205, 214)(150, 215, 202)(156, 218, 220)(165, 210, 221)(167, 217,
226)(170, 227, 179)(171, 191, 192)(174, 200, 233)(177, 234, 181)(178, 194,
222)(180, 223, 216)(182, 231, 199)(184, 185, 189)(187, 213, 243)(188, 245,
246)(193, 247, 236)(197, 255, 250)(198, 211, 201)(203, 212, 204)(207, 262,
240)(219, 256, 267)(224, 244, 269)(225, 265, 248)(228, 273, 239)(229, 270,
274)(230, 237, 252)(232, 266, 268)(235, 261, 241)(238, 272, 271)(249, 254,
253)(257, 279, 260)(258, 263, 280)(259, 278, 264)(275, 283, 284)(281, 282,
285)
C4[ 285, 6 ]
285
-1 2 3 4 5
-2 1 6 7 8
-3 11 1 13 9
-4 1 12 14 10
-5 1 15 17 18
-6 22 2 16 20
-7 23 2 19 21
-8 2 24 27 28
-9 35 3 25 31
-10 36 4 26 32
-11 33 3 37 29
-12 34 4 38 30
-13 3 47 48 39
-14 4 49 40 42
-15 5 60 41 53
-16 55 6 62 43
-17 44 57 5 50
-18 45 59 5 52
-19 56 46 7 63
-20 58 6 51 64
-21 61 7 54 65
-22 66 77 6 76
-23 67 78 69 7
-24 68 83 94 8
-25 70 9 86 97
-26 71 10 87 98
-27 79 90 72 8
-28 82 93 73 8
-29 11 88 99 74
-30 12 89 100 75
-31 101 80 91 9
-32 102 81 92 10
-33 11 103 84 95
-34 12 104 85 96
-35 126 105 128 9
-36 127 106 129 10
-37 11 111 107 130
-38 12 112 108 131
-39 13 160 141 109
-40 110 14 161 142
-41 166 113 146 15
-42 133 14 114 153
-43 167 70 147 16
-44 168 115 148 17
-45 169 116 149 18
-46 170 117 150 19
-47 132 13 118 152
-48 13 159 140 119
-49 155 14 135 120
-50 121 157 137 17
-51 122 158 151 20
-52 123 158 138 18
-53 154 134 124 15
-54 125 84 106 21
-55 156 136 16 171
-56 92 139 172 19
-57 143 17 162 173
-58 154 89 20 174
-59 144 18 163 175
-60 176 145 15 164
-61 165 177 141 21
-62 199 178 201 16
-63 100 200 19 140
-64 179 202 183 20
-65 180 203 184 21
-66 22 221 181 85
-67 198 23 182 194
-68 24 212 223 185
-69 23 115 205 217
-70 25 213 224 43
-71 113 26 225 186
-72 114 27 214 226
-73 28 215 227 186
-74 187 180 29 228
-75 188 180 30 229
-76 22 189 204 216
-77 22 190 129 163
-78 23 191 206 218
-79 220 27 192 208
-80 165 155 193 31
-81 159 194 151 32
-82 99 209 28 195
-83 144 24 95 196
-84 33 54 164 197
-85 66 143 198 34
-86 25 191 207 219
-87 177 26 192 174
-88 154 222 29 139
-89 210 58 30 230
-90 231 211 222 27
-91 232 92 137 31
-92 56 156 91 32
-93 134 233 159 28
-94 210 24 145 234
-95 33 235 83 151
-96 165 34 144 136
-97 231 25 236 250
-98 242 26 237 249
-99 157 82 29 218
-100 256 138 30 63
-101 202 205 238 31
-102 243 216 239 32
-103 33 257 225 150
-104 34 224 258 150
-105 143 209 35 240
-106 209 36 54 241
-107 242 254 37 252
-108 231 122 125 38
-109 244 39 215 263
-110 264 223 40 217
-111 265 112 37 183
-112 111 246 38 185
-113 245 71 41 184
-114 187 269 72 42
-115 44 243 244 69
-116 45 248 117 118
-117 46 116 185 240
-118 188 189 47 116
-119 223 245 48 270
-120 147 49 215 271
-121 214 50 150 272
-122 244 51 249 108
-123 223 213 52 273
-124 246 216 53 274
-125 247 270 108 54
-126 35 226 259 216
-127 36 202 248 260
-128 35 145 161 249
-129 77 36 160 250
-130 200 234 37 171
-131 266 38 261 251
-132 47 268 251 241
-133 267 171 42 240
-134 165 93 53 252
-135 221 157 49 236
-136 55 245 96 218
-137 210 91 247 50
-138 209 100 178 52
-139 88 56 161 163
-140 221 48 237 63
-141 211 39 61 142
-142 253 40 162 141
-143 254 57 105 85
-144 255 59 83 96
-145 201 60 94 128
-146 232 235 41 251
-147 235 248 43 120
-148 44 256 192 262
-149 45 233 191 181
-150 121 46 103 104
-151 81 51 95 162
-152 199 47 172 196
-153 255 247 182 42
-154 88 58 53 219
-155 80 158 268 49
-156 55 92 208 263
-157 99 266 135 50
-158 220 155 51 52
-159 267 48 81 93
-160 210 39 129 206
-161 40 128 139 262
-162 57 151 207 142
-163 77 59 139 261
-164 221 60 84 208
-165 134 80 61 96
-166 190 182 41 195
-167 246 237 173 43
-168 44 199 193 197
-169 242 253 45 230
-170 276 46 228 250
-171 55 275 133 130
-172 56 254 269 152
-173 57 167 278 180
-174 58 279 240 87
-175 265 59 279 215
-176 202 60 269 280
-177 266 213 61 87
-178 211 225 138 62
-179 276 255 239 64
-180 74 173 75 65
-181 66 187 232 149
-182 67 166 282 153
-183 111 184 64 262
-184 113 236 183 65
-185 68 112 193 117
-186 189 71 73 207
-187 244 114 181 74
-188 118 217 75 208
-189 247 118 76 186
-190 77 166 193 229
-191 78 149 283 86
-192 79 148 284 87
-193 80 168 190 185
-194 67 265 201 81
-195 253 166 224 82
-196 236 83 152 274
-197 168 84 227 230
-198 67 222 85 273
-199 168 281 62 152
-200 260 63 130 207
-201 145 62 194 228
-202 176 101 127 64
-203 277 267 258 65
-204 277 256 280 76
-205 101 69 225 261
-206 220 78 246 160
-207 200 162 86 186
-208 188 79 156 164
-209 82 105 138 106
-210 89 137 94 160
-211 90 178 239 141
-212 68 277 219 263
-213 177 123 70 269
-214 121 265 72 241
-215 73 109 120 175
-216 102 124 126 76
-217 110 188 69 252
-218 99 78 136 280
-219 154 212 86 241
-220 79 158 258 206
-221 66 135 140 164
-222 88 198 90 248
-223 110 68 123 119
-224 243 70 104 195
-225 178 103 71 205
-226 245 126 72 230
-227 276 73 273 197
-228 201 170 74 284
-229 190 272 283 75
-230 89 169 226 197
-231 90 97 108 285
-232 264 91 146 181
-233 257 93 149 262
-234 243 268 94 130
-235 146 256 147 95
-236 135 184 97 196
-237 167 255 140 98
-238 253 101 284 274
-239 211 102 179 283
-240 133 105 117 174
-241 132 214 106 219
-242 277 169 107 98
-243 102 234 224 115
-244 187 122 115 109
-245 113 136 226 119
-246 112 167 124 206
-247 189 125 137 153
-248 222 147 116 127
-249 122 128 272 98
-250 170 129 97 252
-251 132 276 146 131
-252 134 107 217 250
-253 169 238 195 142
-254 143 172 271 107
-255 144 179 237 153
-256 100 235 148 204
-257 233 278 103 282
-258 220 104 203 281
-259 266 126 260 282
-260 200 127 259 281
-261 267 205 163 131
-262 233 148 161 183
-263 156 212 282 109
-264 110 232 279 281
-265 111 214 194 175
-266 177 157 259 131
-267 133 159 203 261
-268 132 155 234 278
-269 176 114 213 172
-270 125 271 119 284
-271 254 270 283 120
-272 121 275 249 229
-273 198 275 123 227
-274 275 124 238 196
-275 171 272 273 274
-276 179 170 227 251
-277 242 212 203 204
-278 257 268 173 285
-279 264 174 175 285
-280 176 204 218 285
-281 264 199 258 260
-282 257 182 259 263
-283 191 271 239 229
-284 192 270 238 228
-285 231 278 279 280
0