Graph forms
for C4 [ 243, 31 ] = UG(Cmap(486,14){12,4|9}_18)
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On this page are computer-accessible forms for the graph C4[ 243, 31 ] =
UG(Cmap(486,14){12,4|9}_18).
(I) Following is a form readable by MAGMA:
g:=Graph<243|{ {2, 3}, {242, 243}, {240, 241}, {224, 225}, {222, 223}, {218,
219}, {210, 211}, {204, 205}, {140, 141}, {44, 45}, {28, 29}, {4, 6}, {225,
227}, {188, 190}, {185, 187}, {141, 143}, {1, 2}, {241, 242}, {1, 4}, {224,
229}, {184, 189}, {10, 15}, {8, 13}, {1, 7}, {3, 5}, {99, 101}, {9, 14}, {187,
188}, {67, 68}, {66, 69}, {16, 24}, {226, 234}, {18, 26}, {17, 25}, {150, 159},
{229, 236}, {20, 30}, {1, 10}, {7, 11}, {227, 239}, {5, 8}, {167, 170}, {145,
156}, {2, 12}, {196, 202}, {32, 46}, {19, 29}, {113, 127}, {6, 9}, {97, 110},
{3, 19}, {4, 20}, {34, 51}, {137, 152}, {46, 63}, {42, 59}, {40, 57}, {38, 55},
{36, 53}, {8, 26}, {2, 17}, {138, 153}, {45, 62}, {41, 58}, {37, 54}, {33, 50},
{5, 16}, {231, 242}, {230, 243}, {140, 153}, {109, 120}, {35, 52}, {43, 60}, {3,
27}, {15, 23}, {14, 22}, {13, 21}, {4, 28}, {6, 31}, {70, 95}, {68, 93}, {64,
89}, {11, 16}, {69, 94}, {65, 90}, {110, 117}, {9, 23}, {136, 150}, {12, 18},
{96, 126}, {97, 127}, {39, 56}, {157, 189}, {197, 229}, {25, 56}, {75, 106},
{78, 108}, {198, 228}, {193, 227}, {192, 226}, {137, 171}, {136, 170}, {133,
167}, {79, 109}, {86, 116}, {87, 117}, {90, 120}, {91, 121}, {94, 124}, {95,
125}, {132, 166}, {71, 100}, {207, 236}, {144, 179}, {83, 112}, {128, 164},
{204, 232}, {10, 47}, {145, 180}, {71, 98}, {13, 40}, {84, 113}, {92, 122},
{213, 243}, {207, 233}, {206, 232}, {139, 173}, {138, 172}, {93, 123}, {7, 32},
{206, 233}, {195, 228}, {76, 107}, {24, 63}, {14, 41}, {85, 114}, {130, 165},
{21, 61}, {22, 62}, {205, 228}, {15, 37}, {200, 226}, {193, 235}, {7, 44}, {148,
191}, {77, 102}, {90, 113}, {129, 173}, {6, 43}, {194, 239}, {147, 190}, {74,
103}, {72, 101}, {65, 108}, {27, 53}, {135, 169}, {134, 168}, {66, 108}, {31,
49}, {88, 118}, {89, 119}, {5, 42}, {201, 230}, {146, 189}, {73, 102}, {64,
111}, {136, 184}, {219, 235}, {65, 112}, {216, 233}, {31, 45}, {223, 237}, {151,
164}, {21, 33}, {23, 35}, {22, 34}, {29, 40}, {81, 100}, {11, 61}, {30, 41},
{217, 238}, {156, 171}, {152, 160}, {153, 161}, {203, 241}, {215, 237}, {212,
238}, {11, 48}, {150, 173}, {24, 36}, {211, 239}, {151, 171}, {27, 39}, {26,
38}, {25, 37}, {12, 49}, {211, 238}, {205, 240}, {143, 178}, {82, 111}, {70,
120}, {222, 224}, {220, 226}, {219, 229}, {80, 110}, {75, 116}, {210, 237},
{142, 177}, {157, 221}, {161, 225}, {130, 195}, {173, 236}, {145, 208}, {19,
81}, {146, 208}, {135, 197}, {148, 215}, {160, 227}, {151, 212}, {60, 120},
{180, 240}, {169, 237}, {168, 238}, {8, 64}, {55, 127}, {29, 85}, {10, 66}, {9,
65}, {18, 91}, {32, 105}, {32, 106}, {128, 202}, {59, 119}, {139, 198}, {162,
239}, {59, 117}, {12, 67}, {188, 243}, {165, 234}, {147, 220}, {140, 195}, {37,
106}, {182, 231}, {185, 232}, {15, 92}, {181, 230}, {131, 214}, {17, 71}, {149,
194}, {45, 116}, {155, 194}, {18, 72}, {178, 232}, {19, 73}, {152, 195}, {158,
197}, {20, 72}, {134, 218}, {133, 217}, {148, 201}, {20, 74}, {154, 196}, {132,
228}, {175, 207}, {138, 234}, {141, 236}, {165, 199}, {179, 209}, {178, 208},
{183, 212}, {162, 198}, {163, 199}, {42, 79}, {182, 211}, {168, 205}, {163,
198}, {142, 235}, {47, 73}, {43, 76}, {191, 216}, {181, 210}, {169, 206}, {63,
88}, {50, 85}, {56, 80}, {58, 83}, {190, 215}, {62, 87}, {60, 85}, {47, 68},
{183, 220}, {167, 204}, {61, 86}, {57, 82}, {31, 115}, {13, 96}, {176, 221},
{166, 203}, {14, 97}, {186, 213}, {165, 202}, {59, 84}, {16, 98}, {170, 216},
{17, 99}, {39, 84}, {183, 196}, {28, 104}, {179, 199}, {48, 69}, {186, 204},
{189, 203}, {30, 105}, {49, 70}, {50, 74}, {170, 210}, {169, 209}, {162, 218},
{55, 79}, {54, 78}, {53, 77}, {52, 76}, {51, 75}, {38, 95}, {33, 91}, {48, 74},
{36, 94}, {157, 230}, {174, 213}, {154, 231}, {172, 209}, {34, 92}, {168, 214},
{35, 93}, {175, 208}, {187, 196}, {46, 174}, {72, 200}, {64, 192}, {107, 233},
{67, 192}, {105, 234}, {80, 213}, {71, 193}, {70, 193}, {39, 175}, {75, 199},
{43, 187}, {44, 188}, {26, 139}, {40, 185}, {28, 141}, {99, 242}, {21, 135},
{24, 138}, {41, 186}, {78, 221}, {33, 181}, {36, 176}, {35, 183}, {34, 182},
{27, 140}, {87, 192}, {25, 130}, {94, 194}, {22, 136}, {38, 184}, {23, 137},
{30, 129}, {81, 241}, {49, 144}, {118, 215}, {66, 224}, {67, 225}, {118, 212},
{123, 216}, {114, 214}, {124, 217}, {56, 144}, {97, 200}, {125, 209}, {48, 157},
{100, 201}, {101, 202}, {112, 223}, {126, 206}, {111, 222}, {122, 203}, {51,
129}, {55, 132}, {124, 200}, {54, 131}, {52, 130}, {114, 197}, {42, 146}, {63,
135}, {47, 147}, {58, 134}, {57, 133}, {91, 231}, {115, 207}, {46, 147}, {77,
240}, {86, 235}, {44, 146}, {53, 139}, {103, 166}, {109, 172}, {103, 164}, {92,
149}, {123, 177}, {126, 180}, {115, 184}, {117, 190}, {125, 176}, {104, 166},
{96, 177}, {121, 174}, {127, 167}, {68, 158}, {69, 159}, {88, 131}, {123, 160},
{82, 143}, {124, 161}, {126, 163}, {125, 162}, {80, 176}, {81, 177}, {62, 223},
{78, 175}, {83, 178}, {101, 132}, {103, 134}, {104, 137}, {52, 214}, {98, 128},
{61, 222}, {77, 174}, {102, 133}, {87, 179}, {57, 220}, {122, 159}, {104, 142},
{105, 143}, {122, 156}, {58, 221}, {100, 131}, {112, 151}, {121, 158}, {51,
218}, {113, 152}, {95, 181}, {50, 217}, {84, 191}, {93, 182}, {114, 153}, {119,
156}, {88, 180}, {119, 155}, {54, 219}, {109, 128}, {118, 155}, {116, 154}, {86,
164}, {60, 201}, {107, 158}, {73, 191}, {76, 186}, {79, 185}, {99, 149}, {108,
148}, {121, 129}, {82, 171}, {89, 160}, {98, 155}, {102, 159}, {111, 150}, {89,
163}, {96, 154}, {90, 161}, {106, 145}, {107, 144}, {110, 149}, {115, 142}, {83,
172} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 4, 7, 10)(3, 6, 11, 15)(5, 9, 16, 23)(8, 14, 24, 35)(12, 20, 32, 47)(13,
22, 36, 52)(17, 28, 44, 66)(18, 30, 46, 68)(19, 31, 48, 37)(21, 34, 53, 76)(25,
29, 45, 69)(26, 41, 63, 93)(27, 43, 61, 92)(33, 51, 77, 107)(38, 58, 88,
123)(39, 60, 86, 122)(40, 62, 94, 130)(42, 65, 98, 137)(49, 74, 106, 73)(50, 75,
102, 144)(54, 81, 115, 157)(55, 83, 118, 160)(56, 85, 116, 159)(57, 87, 124,
165)(59, 90, 128, 171)(64, 97, 138, 183)(67, 72, 105, 147)(70, 103, 145,
191)(71, 104, 146, 108)(78, 100, 142, 189)(79, 112, 155, 152)(80, 114, 154,
150)(82, 117, 161, 202)(84, 120, 164, 156)(89, 127, 172, 212)(91, 129, 174,
158)(95, 134, 180, 216)(96, 136, 176, 214)(99, 141, 188, 224)(101, 143, 190,
225)(109, 151, 119, 113)(110, 153, 196, 111)(125, 168, 126, 170)(131, 177, 184,
221)(132, 178, 215, 227)(133, 179, 217, 199)(135, 182, 139, 186)(140, 187, 222,
149)(148, 193, 166, 208)(162, 205, 206, 210)(163, 167, 209, 238)(169, 211, 198,
204)(173, 213, 197, 231)(175, 201, 235, 203)(181, 218, 240, 233)(185, 223, 194,
195)(192, 200, 234, 220)(207, 230, 219, 241)(228, 232, 237, 239)(229, 242, 236,
243) (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, 17, 99, 242, 243, 188, 44, 7)(3, 25, 101, 241, 213, 187, 146, 32,
4)(5, 37, 72, 81, 80, 196, 189, 46, 6)(8, 54, 200, 177, 176, 183, 184, 63,
9)(10, 12, 71, 149, 231, 230, 190, 45, 11)(13, 78, 226, 142, 36, 35, 38, 88,
14)(15, 18, 100, 110, 154, 157, 147, 31, 16)(19, 56, 202, 203, 174, 43, 42, 106,
20)(21, 108, 192, 235, 94, 93, 95, 118, 22)(23, 26, 131, 97, 96, 221, 220, 115,
24)(27, 130, 132, 240, 186, 185, 208, 105, 28)(29, 39, 165, 166, 77, 76, 79,
145, 30)(33, 148, 87, 86, 69, 68, 70, 155, 34)(40, 175, 234, 104, 53, 52, 55,
180, 41)(47, 49, 98, 92, 91, 201, 117, 116, 48)(50, 191, 179, 164, 159, 158,
120, 119, 51)(57, 207, 138, 137, 139, 214, 127, 126, 58)(59, 75, 74, 73, 144,
128, 122, 121, 60)(61, 66, 67, 193, 194, 182, 181, 215, 62)(64, 219, 124, 123,
125, 212, 136, 135, 65)(82, 236, 153, 152, 198, 168, 167, 206, 83)(84, 199, 103,
102, 107, 109, 156, 129, 85)(89, 218, 217, 216, 209, 151, 150, 197, 90)(111,
229, 161, 160, 162, 238, 170, 169, 112)(113, 163, 134, 133, 233, 172, 171, 173,
114)(140, 195, 228, 205, 204, 232, 178, 143, 141)(210, 237, 223, 222, 224, 225,
227, 239, 211)
C4[ 243, 31 ]
243
-1 2 4 7 10
-2 1 12 3 17
-3 2 5 27 19
-4 1 6 28 20
-5 3 16 8 42
-6 4 9 31 43
-7 11 44 1 32
-8 13 26 5 64
-9 23 14 6 65
-10 66 1 47 15
-11 48 16 61 7
-12 67 2 49 18
-13 40 8 96 21
-14 22 41 9 97
-15 23 37 92 10
-16 11 24 5 98
-17 99 2 25 71
-18 12 91 26 72
-19 3 81 29 73
-20 4 72 30 74
-21 33 13 135 61
-22 34 14 136 62
-23 35 15 137 9
-24 36 16 138 63
-25 56 37 17 130
-26 38 18 139 8
-27 3 39 140 53
-28 4 104 29 141
-29 28 40 19 85
-30 105 41 129 20
-31 45 49 115 6
-32 46 105 7 106
-33 91 181 50 21
-34 22 92 182 51
-35 23 93 183 52
-36 176 24 94 53
-37 25 15 106 54
-38 55 26 95 184
-39 56 27 84 175
-40 13 57 29 185
-41 14 58 30 186
-42 79 146 59 5
-43 187 60 6 76
-44 45 188 146 7
-45 44 116 62 31
-46 147 63 174 32
-47 68 147 73 10
-48 11 69 157 74
-49 12 144 70 31
-50 33 74 85 217
-51 34 129 75 218
-52 35 214 130 76
-53 77 36 27 139
-54 78 37 131 219
-55 132 79 38 127
-56 144 25 80 39
-57 220 133 82 40
-58 221 134 83 41
-59 84 117 42 119
-60 201 85 43 120
-61 11 222 86 21
-62 22 45 223 87
-63 88 24 46 135
-64 89 111 192 8
-65 90 112 9 108
-66 69 224 108 10
-67 12 68 192 225
-68 67 47 158 93
-69 66 48 159 94
-70 49 193 95 120
-71 100 17 193 98
-72 101 200 18 20
-73 47 102 191 19
-74 48 103 50 20
-75 199 116 51 106
-76 52 107 43 186
-77 102 53 174 240
-78 221 108 54 175
-79 55 42 185 109
-80 110 176 56 213
-81 100 177 19 241
-82 143 111 57 171
-83 112 178 58 172
-84 113 59 191 39
-85 114 60 50 29
-86 235 61 116 164
-87 179 192 62 117
-88 180 63 118 131
-89 160 64 119 163
-90 113 161 65 120
-91 33 121 231 18
-92 34 122 15 149
-93 35 68 123 182
-94 36 69 124 194
-95 70 125 38 181
-96 154 177 13 126
-97 110 200 14 127
-98 155 16 71 128
-99 242 101 17 149
-100 201 81 71 131
-101 99 132 202 72
-102 77 133 159 73
-103 166 134 74 164
-104 166 137 28 142
-105 143 234 30 32
-106 145 37 75 32
-107 144 233 158 76
-108 66 78 148 65
-109 79 128 172 120
-110 80 149 117 97
-111 222 82 150 64
-112 223 83 151 65
-113 90 127 84 152
-114 214 85 153 197
-115 184 31 207 142
-116 154 45 75 86
-117 110 190 59 87
-118 88 155 212 215
-119 89 155 156 59
-120 90 70 60 109
-121 91 158 129 174
-122 156 92 159 203
-123 177 93 160 216
-124 200 94 161 217
-125 176 209 95 162
-126 180 96 206 163
-127 55 167 113 97
-128 202 98 109 164
-129 121 51 30 173
-130 165 25 52 195
-131 88 100 214 54
-132 55 166 101 228
-133 57 167 102 217
-134 58 168 103 218
-135 169 63 21 197
-136 22 170 150 184
-137 23 104 171 152
-138 24 234 172 153
-139 198 26 173 53
-140 27 195 141 153
-141 143 236 28 140
-142 177 235 104 115
-143 178 82 105 141
-144 56 179 49 107
-145 156 180 106 208
-146 44 189 42 208
-147 220 46 47 190
-148 201 191 215 108
-149 99 110 92 194
-150 111 136 159 173
-151 112 212 171 164
-152 113 137 160 195
-153 114 138 161 140
-154 231 116 96 196
-155 194 118 119 98
-156 122 145 171 119
-157 221 189 48 230
-158 121 68 107 197
-159 122 69 102 150
-160 89 123 227 152
-161 90 124 225 153
-162 198 125 239 218
-163 198 89 199 126
-164 103 128 151 86
-165 199 234 202 130
-166 132 103 104 203
-167 133 170 127 204
-168 134 214 205 238
-169 209 135 237 206
-170 210 167 136 216
-171 156 82 137 151
-172 209 83 138 109
-173 236 139 150 129
-174 77 121 46 213
-175 78 39 207 208
-176 221 36 80 125
-177 123 81 96 142
-178 143 232 83 208
-179 209 144 199 87
-180 88 145 126 240
-181 33 210 95 230
-182 231 34 211 93
-183 220 35 212 196
-184 189 136 38 115
-185 187 232 79 40
-186 213 204 41 76
-187 188 185 196 43
-188 44 187 243 190
-189 146 157 203 184
-190 188 147 215 117
-191 148 73 84 216
-192 67 226 64 87
-193 70 235 71 227
-194 155 94 149 239
-195 140 228 130 152
-196 154 187 202 183
-197 135 114 158 229
-198 139 162 228 163
-199 165 179 75 163
-200 124 72 226 97
-201 100 60 148 230
-202 165 101 128 196
-203 122 166 189 241
-204 232 167 205 186
-205 168 204 228 240
-206 232 233 169 126
-207 233 115 236 175
-208 145 178 146 175
-209 179 125 169 172
-210 211 170 181 237
-211 210 182 238 239
-212 183 238 118 151
-213 243 80 174 186
-214 168 114 52 131
-215 190 148 237 118
-216 123 233 191 170
-217 133 124 50 238
-218 134 51 162 219
-219 235 218 229 54
-220 57 147 226 183
-221 176 78 58 157
-222 111 223 224 61
-223 112 222 237 62
-224 66 222 225 229
-225 67 224 161 227
-226 220 200 234 192
-227 225 160 193 239
-228 132 198 205 195
-229 224 236 197 219
-230 243 157 201 181
-231 154 242 91 182
-232 178 204 206 185
-233 216 107 206 207
-234 165 105 138 226
-235 193 86 142 219
-236 173 141 207 229
-237 210 223 169 215
-238 211 168 212 217
-239 211 194 227 162
-240 77 180 205 241
-241 242 81 203 240
-242 99 231 243 241
-243 242 188 213 230
0