Graph forms
for C4 [ 273, 13 ] = UG(Rmap(546,85){7,4|14}_12)
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On this page are computer-accessible forms for the graph C4[ 273, 13 ] =
UG(Rmap(546,85){7,4|14}_12).
(I) Following is a form readable by MAGMA:
g:=Graph<273|{ {32, 33}, {272, 273}, {174, 175}, {108, 109}, {98, 99}, {84, 85},
{74, 75}, {126, 127}, {152, 153}, {1, 3}, {265, 267}, {204, 206}, {61, 63}, {1,
2}, {216, 219}, {185, 186}, {45, 46}, {1, 5}, {224, 228}, {9, 13}, {2, 7}, {266,
271}, {264, 269}, {251, 254}, {3, 6}, {2, 4}, {8, 15}, {3, 11}, {213, 221}, {20,
28}, {1, 8}, {7, 14}, {65, 75}, {196, 206}, {181, 191}, {69, 79}, {149, 159},
{6, 13}, {215, 220}, {208, 219}, {16, 28}, {258, 270}, {178, 190}, {18, 30},
{17, 29}, {146, 158}, {4, 9}, {260, 265}, {209, 220}, {84, 89}, {2, 12}, {242,
252}, {5, 10}, {20, 27}, {112, 127}, {39, 55}, {229, 245}, {3, 18}, {6, 23},
{170, 187}, {42, 56}, {235, 249}, {139, 153}, {141, 159}, {12, 31}, {205, 222},
{194, 209}, {161, 178}, {169, 186}, {4, 16}, {15, 27}, {5, 17}, {34, 55}, {107,
126}, {135, 145}, {227, 245}, {140, 154}, {166, 177}, {71, 95}, {10, 19}, {12,
21}, {236, 246}, {35, 56}, {233, 242}, {229, 254}, {173, 182}, {165, 185}, {4,
25}, {226, 255}, {203, 214}, {199, 218}, {40, 53}, {36, 57}, {14, 19}, {8, 22},
{231, 249}, {225, 255}, {5, 26}, {271, 272}, {232, 247}, {198, 217}, {197, 218},
{41, 54}, {37, 58}, {11, 20}, {7, 24}, {135, 152}, {143, 144}, {13, 45}, {195,
227}, {71, 103}, {70, 102}, {15, 46}, {211, 242}, {204, 237}, {68, 101}, {66,
99}, {17, 48}, {134, 167}, {25, 59}, {148, 182}, {149, 183}, {7, 36}, {192,
227}, {76, 111}, {6, 35}, {212, 241}, {210, 247}, {193, 228}, {14, 40}, {26,
60}, {67, 100}, {192, 231}, {94, 121}, {88, 127}, {9, 32}, {201, 224}, {31, 54},
{11, 34}, {150, 191}, {21, 63}, {79, 101}, {10, 33}, {193, 234}, {30, 53}, {216,
244}, {8, 37}, {199, 234}, {80, 125}, {19, 62}, {76, 98}, {67, 108}, {81, 126},
{131, 172}, {132, 171}, {145, 190}, {13, 61}, {214, 230}, {132, 180}, {22, 39},
{83, 98}, {26, 43}, {24, 41}, {78, 124}, {223, 237}, {211, 225}, {129, 179},
{21, 38}, {25, 42}, {29, 41}, {87, 99}, {142, 187}, {222, 235}, {77, 123}, {141,
186}, {9, 49}, {207, 247}, {12, 52}, {11, 51}, {10, 50}, {128, 184}, {195, 250},
{207, 246}, {28, 38}, {203, 241}, {29, 39}, {93, 102}, {64, 124}, {130, 190},
{133, 185}, {18, 44}, {196, 250}, {16, 47}, {204, 243}, {202, 245}, {23, 40},
{61, 125}, {62, 126}, {44, 109}, {48, 114}, {181, 247}, {45, 110}, {63, 123},
{156, 216}, {24, 93}, {38, 99}, {26, 95}, {158, 219}, {19, 84}, {41, 110}, {40,
111}, {25, 94}, {136, 207}, {61, 116}, {189, 244}, {131, 202}, {150, 223}, {31,
85}, {190, 244}, {53, 127}, {15, 68}, {23, 92}, {149, 222}, {38, 106}, {45, 97},
{155, 215}, {14, 67}, {175, 226}, {62, 115}, {22, 91}, {20, 89}, {39, 105},
{184, 246}, {52, 122}, {46, 96}, {162, 236}, {21, 90}, {188, 243}, {183, 248},
{43, 100}, {157, 210}, {164, 235}, {148, 196}, {168, 248}, {138, 216}, {30, 77},
{142, 221}, {146, 193}, {167, 243}, {16, 69}, {34, 119}, {18, 71}, {133, 208},
{22, 64}, {180, 226}, {23, 65}, {137, 223}, {17, 70}, {27, 76}, {170, 253}, {49,
105}, {56, 96}, {51, 107}, {50, 106}, {163, 250}, {24, 66}, {165, 255}, {35,
120}, {58, 97}, {52, 104}, {166, 250}, {168, 244}, {36, 121}, {46, 112}, {60,
98}, {47, 113}, {137, 215}, {37, 122}, {161, 254}, {143, 239}, {181, 213}, {155,
251}, {156, 252}, {55, 86}, {42, 72}, {180, 214}, {43, 73}, {134, 228}, {164,
198}, {139, 232}, {47, 75}, {54, 82}, {52, 80}, {151, 243}, {157, 249}, {169,
205}, {57, 92}, {128, 229}, {140, 233}, {167, 194}, {44, 74}, {147, 245}, {163,
197}, {161, 198}, {162, 197}, {29, 116}, {33, 72}, {32, 73}, {31, 118}, {160,
201}, {183, 221}, {30, 117}, {176, 219}, {136, 228}, {138, 230}, {177, 220},
{179, 222}, {151, 249}, {28, 115}, {184, 215}, {143, 224}, {173, 221}, {35, 82},
{59, 74}, {144, 225}, {147, 226}, {171, 217}, {160, 211}, {37, 81}, {191, 203},
{32, 86}, {33, 87}, {159, 233}, {172, 218}, {27, 108}, {174, 217}, {57, 78},
{36, 83}, {129, 246}, {135, 255}, {132, 253}, {173, 212}, {34, 88}, {133, 254},
{48, 76}, {51, 79}, {50, 78}, {49, 77}, {54, 75}, {55, 74}, {62, 64}, {182,
200}, {142, 240}, {144, 238}, {107, 235}, {78, 204}, {104, 234}, {111, 236},
{117, 240}, {119, 242}, {86, 208}, {87, 209}, {118, 241}, {88, 210}, {89, 211},
{59, 176}, {93, 214}, {60, 177}, {90, 212}, {91, 213}, {103, 232}, {115, 231},
{58, 175}, {56, 174}, {116, 227}, {123, 224}, {83, 207}, {80, 205}, {112, 237},
{114, 239}, {124, 225}, {81, 206}, {113, 238}, {123, 217}, {48, 147}, {100,
199}, {96, 195}, {57, 157}, {42, 143}, {51, 150}, {49, 148}, {109, 200}, {124,
218}, {50, 149}, {110, 201}, {105, 197}, {106, 198}, {59, 137}, {53, 134}, {119,
196}, {63, 139}, {60, 138}, {117, 195}, {101, 220}, {114, 203}, {120, 193}, {58,
128}, {112, 202}, {122, 192}, {43, 144}, {121, 194}, {44, 145}, {47, 146}, {68,
134}, {85, 151}, {71, 133}, {69, 135}, {125, 187}, {80, 155}, {64, 140}, {84,
152}, {66, 142}, {65, 141}, {81, 156}, {70, 136}, {79, 129}, {113, 191}, {72,
153}, {73, 154}, {110, 189}, {111, 188}, {118, 165}, {104, 189}, {108, 185},
{109, 184}, {89, 128}, {91, 130}, {96, 186}, {122, 160}, {90, 129}, {107, 176},
{103, 188}, {95, 132}, {125, 166}, {94, 131}, {105, 138}, {106, 137}, {77, 169},
{102, 130}, {121, 159}, {92, 187}, {113, 153}, {114, 154}, {115, 155}, {116,
156}, {117, 157}, {118, 158}, {97, 136}, {72, 163}, {73, 164}, {120, 150}, {104,
152}, {66, 179}, {70, 183}, {68, 181}, {65, 178}, {103, 148}, {100, 151}, {69,
182}, {82, 167}, {88, 173}, {119, 130}, {101, 147}, {67, 180}, {102, 158}, {90,
163}, {92, 165}, {82, 168}, {83, 168}, {97, 154}, {93, 166}, {87, 172}, {120,
131}, {86, 171}, {95, 162}, {85, 170}, {94, 161}, {91, 164}, {139, 256}, {140,
257}, {141, 258}, {145, 259}, {146, 260}, {172, 270}, {169, 268}, {170, 268},
{171, 269}, {162, 267}, {160, 266}, {175, 258}, {174, 257}, {188, 264}, {189,
265}, {179, 261}, {176, 263}, {177, 262}, {178, 271}, {205, 269}, {208, 272},
{206, 270}, {209, 272}, {200, 266}, {199, 256}, {200, 256}, {194, 267}, {201,
261}, {202, 262}, {223, 273}, {192, 273}, {212, 262}, {213, 263}, {210, 269},
{234, 264}, {231, 260}, {236, 271}, {237, 265}, {239, 264}, {238, 262}, {239,
263}, {229, 268}, {230, 268}, {233, 259}, {238, 258}, {232, 261}, {241, 259},
{248, 266}, {240, 259}, {230, 273}, {252, 267}, {248, 257}, {253, 260}, {251,
257}, {253, 263}, {252, 256}, {240, 270}, {251, 261} }>;
(II) A more general form is to represent the graph as the orbit of {32, 33}
under the group generated by the following permutations:
a: (2, 8)(4, 15)(6, 11)(7, 22)(9, 27)(10, 17)(12, 37)(13, 20)(14, 39)(16,
46)(19, 29)(21, 58)(23, 34)(24, 64)(25, 68)(28, 45)(30, 44)(31, 81)(32, 76)(33,
48)(35, 51)(36, 91)(38, 97)(40, 55)(41, 62)(42, 101)(43, 60)(47, 112)(49,
108)(50, 70)(52, 122)(53, 74)(54, 126)(56, 79)(57, 130)(59, 134)(61, 89)(63,
128)(65, 88)(66, 140)(67, 105)(69, 96)(72, 147)(73, 98)(75, 127)(77, 109)(78,
102)(80, 160)(82, 107)(83, 164)(84, 116)(85, 156)(86, 111)(87, 114)(90, 175)(92,
119)(93, 124)(94, 181)(99, 154)(100, 138)(103, 133)(104, 192)(106, 136)(110,
115)(113, 202)(117, 145)(118, 206)(120, 150)(121, 213)(123, 184)(125, 211)(129,
174)(131, 191)(132, 162)(135, 195)(137, 228)(139, 229)(141, 173)(142, 233)(143,
220)(144, 177)(146, 237)(148, 185)(149, 183)(151, 216)(152, 227)(153, 245)(155,
201)(157, 190)(158, 204)(159, 221)(161, 247)(163, 226)(165, 196)(166, 225)(167,
176)(168, 235)(169, 200)(170, 252)(171, 236)(172, 203)(178, 210)(179, 257)(180,
197)(182, 186)(187, 242)(188, 208)(189, 231)(193, 223)(194, 263)(198, 207)(199,
230)(205, 266)(209, 239)(212, 258)(214, 218)(215, 224)(217, 246)(219, 243)(222,
248)(232, 254)(234, 273)(238, 262)(240, 259)(241, 270)(244, 249)(250, 255)(251,
261)(253, 267)(256, 268)(260, 265)(264, 272)(269, 271) (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, 7)(6, 9)(8, 12)(10, 14)(11, 16)(15, 21)(17, 24)(18, 25)(20,
28)(22, 31)(23, 32)(26, 36)(27, 38)(29, 41)(30, 42)(33, 40)(34, 47)(35, 49)(37,
52)(39, 54)(43, 57)(44, 59)(45, 61)(46, 63)(48, 66)(50, 67)(51, 69)(53, 72)(55,
75)(56, 77)(58, 80)(60, 83)(62, 84)(64, 85)(65, 86)(68, 90)(70, 93)(71, 94)(73,
92)(76, 99)(78, 100)(81, 104)(82, 105)(87, 111)(88, 113)(89, 115)(91, 118)(95,
121)(96, 123)(97, 125)(101, 129)(103, 131)(106, 108)(107, 135)(109, 137)(110,
116)(112, 139)(114, 142)(117, 143)(119, 146)(120, 148)(124, 151)(126, 152)(127,
153)(128, 155)(130, 158)(132, 159)(133, 161)(134, 163)(136, 166)(138, 168)(140,
170)(141, 171)(144, 157)(145, 176)(147, 179)(149, 180)(150, 182)(154, 187)(156,
189)(160, 192)(162, 194)(164, 165)(167, 197)(169, 174)(172, 188)(173, 191)(175,
205)(177, 207)(178, 208)(181, 212)(183, 214)(184, 215)(185, 198)(186, 217)(190,
219)(193, 196)(195, 224)(199, 204)(200, 223)(201, 227)(202, 232)(203, 221)(206,
234)(209, 236)(210, 238)(211, 231)(213, 241)(216, 244)(218, 243)(220, 246)(222,
226)(225, 249)(228, 250)(229, 251)(230, 248)(233, 253)(235, 255)(237, 256)(239,
240)(242, 260)(245, 261)(247, 262)(252, 265)(257, 268)(258, 269)(259, 263)(264,
270)(266, 273)(271, 272)
c: (2, 5, 8, 3)(4, 10, 22, 11)(6, 7, 17, 15)(9, 19, 39, 20)(12, 26, 37, 18)(13,
14, 29, 27)(16, 33, 64, 34)(21, 43, 81, 44)(23, 24, 48, 46)(25, 50, 91, 51)(28,
32, 62, 55)(30, 31, 60, 58)(35, 36, 70, 68)(38, 73, 126, 74)(40, 41, 76, 45)(42,
78, 130, 79)(47, 87, 140, 88)(49, 84, 105, 89)(52, 95, 122, 71)(53, 54, 98,
97)(56, 57, 102, 101)(59, 106, 164, 107)(61, 67, 116, 108)(63, 100, 156,
109)(65, 66, 114, 112)(69, 72, 124, 119)(75, 99, 154, 127)(77, 85, 138, 128)(80,
132, 192, 133)(82, 83, 136, 134)(86, 115)(90, 144, 206, 145)(92, 93, 147,
96)(94, 149, 213, 150)(103, 104, 162, 160)(110, 111)(113, 172, 233, 173)(117,
118, 177, 175)(120, 121, 183, 181)(123, 151, 216, 184)(125, 180, 227, 185)(129,
143, 204, 190)(131, 159, 221, 191)(135, 163, 225, 196)(137, 198, 235, 176)(139,
199, 252, 200)(141, 142, 203, 202)(146, 209, 257, 210)(148, 152, 197, 211)(153,
218, 242, 182)(155, 171, 231, 208)(157, 158, 220, 174)(161, 222, 263, 223)(165,
166, 226, 195)(167, 168, 207, 228)(169, 170, 230, 229)(178, 179, 239, 237)(186,
187, 214, 245)(188, 189, 236, 201)(193, 194, 248, 247)(205, 253, 273, 254)(212,
238, 270, 259)(215, 217, 249, 219)(224, 243, 244, 246)(232, 234, 267, 266)(240,
241, 262, 258)(250, 255)(251, 269, 260, 272)(261, 264, 265, 271)
C4[ 273, 13 ]
273
-1 2 3 5 8
-2 1 12 4 7
-3 11 1 6 18
-4 2 25 16 9
-5 1 26 17 10
-6 23 13 35 3
-7 2 24 14 36
-8 22 1 15 37
-9 13 4 49 32
-10 33 5 50 19
-11 34 3 51 20
-12 2 52 31 21
-13 45 6 61 9
-14 67 7 40 19
-15 46 68 27 8
-16 47 69 4 28
-17 48 70 5 29
-18 44 3 71 30
-19 14 62 84 10
-20 11 89 27 28
-21 12 90 38 63
-22 91 39 8 64
-23 92 6 40 65
-24 66 93 7 41
-25 4 59 94 42
-26 5 60 95 43
-27 15 20 108 76
-28 16 38 115 20
-29 17 39 116 41
-30 77 18 117 53
-31 12 85 118 54
-32 33 73 9 86
-33 72 10 32 87
-34 11 55 88 119
-35 56 82 6 120
-36 121 57 83 7
-37 122 58 81 8
-38 99 28 106 21
-39 22 55 105 29
-40 23 111 14 53
-41 110 24 29 54
-42 143 56 25 72
-43 100 144 26 73
-44 145 18 74 109
-45 110 13 46 97
-46 45 112 15 96
-47 113 146 16 75
-48 114 147 17 76
-49 77 148 105 9
-50 78 149 106 10
-51 11 79 150 107
-52 12 122 80 104
-53 134 127 40 30
-54 82 41 31 75
-55 34 39 74 86
-56 35 96 42 174
-57 78 36 157 92
-58 37 128 97 175
-59 176 25 137 74
-60 177 26 138 98
-61 13 125 116 63
-62 115 126 19 64
-63 123 61 139 21
-64 22 124 62 140
-65 23 178 75 141
-66 99 24 179 142
-67 100 14 180 108
-68 101 134 15 181
-69 79 135 16 182
-70 102 136 17 183
-71 133 103 18 95
-72 33 42 163 153
-73 154 32 43 164
-74 44 55 59 75
-75 47 74 54 65
-76 111 48 27 98
-77 123 169 49 30
-78 57 124 50 204
-79 101 69 51 129
-80 155 125 205 52
-81 156 37 126 206
-82 35 167 168 54
-83 36 168 207 98
-84 89 19 85 152
-85 170 84 151 31
-86 55 171 32 208
-87 33 99 209 172
-88 34 210 127 173
-89 211 84 128 20
-90 212 129 163 21
-91 22 213 130 164
-92 165 187 23 57
-93 166 24 102 214
-94 121 25 161 131
-95 132 26 71 162
-96 56 46 195 186
-97 154 45 58 136
-98 99 60 83 76
-99 66 38 87 98
-100 67 199 151 43
-101 220 68 79 147
-102 70 158 93 130
-103 188 232 71 148
-104 189 234 52 152
-105 49 39 138 197
-106 198 38 137 50
-107 176 235 126 51
-108 67 27 185 109
-109 44 200 184 108
-110 45 189 201 41
-111 188 236 40 76
-112 46 202 127 237
-113 47 191 238 153
-114 154 48 203 239
-115 231 155 28 62
-116 156 61 29 227
-117 157 30 195 240
-118 165 158 31 241
-119 242 34 130 196
-120 35 193 150 131
-121 36 159 94 194
-122 37 192 160 52
-123 77 224 63 217
-124 78 225 64 218
-125 187 166 80 61
-126 81 127 62 107
-127 88 112 126 53
-128 89 58 184 229
-129 79 90 179 246
-130 91 102 190 119
-131 202 94 172 120
-132 253 180 171 95
-133 254 71 185 208
-134 68 167 228 53
-135 145 255 69 152
-136 70 228 97 207
-137 223 59 215 106
-138 60 105 216 230
-139 232 256 63 153
-140 154 233 257 64
-141 159 258 65 186
-142 66 187 221 240
-143 144 224 239 42
-144 143 225 238 43
-145 44 135 190 259
-146 47 158 193 260
-147 101 245 48 226
-148 103 49 182 196
-149 222 159 50 183
-150 223 191 51 120
-151 100 243 249 85
-152 135 104 84 153
-153 113 72 139 152
-154 114 73 140 97
-155 80 115 215 251
-156 81 116 216 252
-157 210 57 117 249
-158 102 146 118 219
-159 121 233 149 141
-160 122 211 266 201
-161 198 254 178 94
-162 267 236 95 197
-163 90 72 250 197
-164 198 91 235 73
-165 255 92 118 185
-166 177 125 93 250
-167 243 134 82 194
-168 244 82 83 248
-169 77 268 205 186
-170 187 253 268 85
-171 132 269 217 86
-172 270 218 87 131
-173 88 221 212 182
-174 56 257 217 175
-175 58 258 226 174
-176 59 107 219 263
-177 220 166 60 262
-178 190 161 271 65
-179 66 222 129 261
-180 132 67 214 226
-181 68 191 213 247
-182 200 69 148 173
-183 221 70 149 248
-184 246 215 128 109
-185 165 133 108 186
-186 169 96 141 185
-187 92 125 170 142
-188 264 111 243 103
-189 110 265 244 104
-190 145 178 244 130
-191 113 181 203 150
-192 231 122 227 273
-193 146 234 228 120
-194 121 209 167 267
-195 117 227 96 250
-196 148 206 250 119
-197 105 162 163 218
-198 106 161 217 164
-199 100 234 256 218
-200 266 256 182 109
-201 110 224 160 261
-202 112 245 262 131
-203 114 191 214 241
-204 78 243 237 206
-205 222 80 169 269
-206 81 204 270 196
-207 136 246 247 83
-208 133 272 86 219
-209 220 194 272 87
-210 88 157 247 269
-211 242 89 225 160
-212 90 173 262 241
-213 221 91 181 263
-214 180 93 203 230
-215 220 155 137 184
-216 156 244 138 219
-217 198 123 171 174
-218 199 124 172 197
-219 176 158 216 208
-220 209 177 101 215
-221 213 183 173 142
-222 179 235 149 205
-223 137 237 150 273
-224 143 123 201 228
-225 144 211 255 124
-226 255 147 180 175
-227 245 192 116 195
-228 134 136 224 193
-229 254 245 268 128
-230 268 214 138 273
-231 115 192 249 260
-232 103 247 139 261
-233 242 159 259 140
-234 264 199 104 193
-235 222 249 107 164
-236 111 246 271 162
-237 265 112 223 204
-238 144 113 258 262
-239 143 264 114 263
-240 259 270 117 142
-241 212 203 259 118
-242 211 233 119 252
-243 188 167 204 151
-244 189 168 190 216
-245 147 202 227 229
-246 236 129 184 207
-247 210 232 181 207
-248 266 168 257 183
-249 231 157 235 151
-250 166 195 163 196
-251 155 254 257 261
-252 242 156 256 267
-253 132 170 260 263
-254 133 161 229 251
-255 165 135 225 226
-256 199 200 139 252
-257 248 140 174 251
-258 270 238 141 175
-259 145 233 240 241
-260 231 253 265 146
-261 232 179 201 251
-262 177 212 202 238
-263 176 253 213 239
-264 188 234 269 239
-265 189 267 237 260
-266 200 160 248 271
-267 265 194 162 252
-268 169 170 229 230
-269 264 210 171 205
-270 258 172 206 240
-271 178 266 236 272
-272 209 271 273 208
-273 223 192 272 230
0