Graph forms
for C4 [ 240, 57 ] = KE_60(1,3,10,13,19)
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On this page are computer-accessible forms for the graph C4[ 240, 57 ] =
KE_60(1,3,10,13,19).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {2, 3}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {48,
49}, {46, 47}, {44, 45}, {42, 43}, {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}, {1, 2}, {57, 58},
{53, 54}, {49, 50}, {45, 46}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22},
{25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {3, 4}, {59, 60}, {51, 52},
{43, 44}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {112, 122}, {113, 123}, {116,
126}, {117, 127}, {114, 124}, {115, 125}, {7, 8}, {55, 56}, {23, 24}, {39, 40},
{192, 211}, {204, 223}, {200, 219}, {196, 215}, {193, 212}, {203, 222}, {201,
220}, {195, 214}, {111, 121}, {194, 213}, {202, 221}, {197, 216}, {199, 218},
{15, 16}, {198, 217}, {47, 48}, {192, 233}, {198, 239}, {196, 237}, {194, 235},
{193, 234}, {197, 238}, {205, 224}, {221, 240}, {207, 226}, {195, 236}, {206,
225}, {208, 227}, {220, 239}, {216, 235}, {212, 231}, {209, 228}, {219, 238},
{217, 236}, {211, 230}, {199, 240}, {218, 237}, {210, 229}, {4, 61}, {6, 63},
{5, 62}, {64, 124}, {67, 127}, {66, 126}, {65, 125}, {128, 188}, {129, 189},
{130, 190}, {131, 191}, {1, 60}, {215, 234}, {213, 232}, {31, 32}, {214, 233},
{61, 121}, {180, 240}, {175, 235}, {174, 234}, {173, 233}, {172, 232}, {167,
227}, {166, 226}, {165, 225}, {164, 224}, {159, 219}, {158, 218}, {157, 217},
{156, 216}, {151, 211}, {150, 210}, {149, 209}, {148, 208}, {143, 203}, {142,
202}, {141, 201}, {140, 200}, {135, 195}, {63, 123}, {62, 122}, {132, 192},
{133, 193}, {134, 194}, {7, 64}, {55, 112}, {47, 104}, {15, 72}, {23, 80}, {31,
88}, {39, 96}, {8, 65}, {60, 117}, {58, 115}, {56, 113}, {46, 103}, {44, 101},
{42, 99}, {10, 67}, {12, 69}, {14, 71}, {24, 81}, {26, 83}, {28, 85}, {30, 87},
{40, 97}, {9, 66}, {57, 114}, {45, 102}, {13, 70}, {25, 82}, {29, 86}, {41, 98},
{136, 196}, {171, 231}, {170, 230}, {169, 229}, {168, 228}, {155, 215}, {154,
214}, {153, 213}, {152, 212}, {139, 199}, {138, 198}, {137, 197}, {11, 68}, {59,
116}, {43, 100}, {27, 84}, {183, 224}, {191, 232}, {16, 73}, {190, 231}, {188,
229}, {186, 227}, {184, 225}, {54, 111}, {52, 109}, {50, 107}, {48, 105}, {18,
75}, {20, 77}, {22, 79}, {17, 74}, {189, 230}, {185, 226}, {53, 110}, {49, 106},
{21, 78}, {144, 204}, {179, 239}, {178, 238}, {177, 237}, {176, 236}, {147,
207}, {146, 206}, {145, 205}, {19, 76}, {187, 228}, {51, 108}, {182, 223}, {181,
222}, {189, 208}, {191, 210}, {190, 209}, {184, 203}, {188, 207}, {2, 119},
{187, 206}, {185, 204}, {1, 118}, {186, 205}, {1, 121}, {2, 122}, {3, 123}, {4,
124}, {5, 125}, {6, 126}, {7, 127}, {32, 89}, {34, 91}, {36, 93}, {38, 95}, {3,
120}, {33, 90}, {37, 94}, {160, 220}, {163, 223}, {162, 222}, {161, 221}, {181,
200}, {183, 202}, {35, 92}, {182, 201}, {64, 197}, {72, 205}, {66, 199}, {74,
207}, {80, 213}, {82, 215}, {88, 221}, {90, 223}, {96, 229}, {98, 231}, {104,
237}, {106, 239}, {65, 198}, {73, 206}, {81, 214}, {89, 222}, {97, 230}, {105,
238}, {8, 128}, {60, 180}, {59, 179}, {58, 178}, {57, 177}, {56, 176}, {47,
167}, {46, 166}, {45, 165}, {44, 164}, {43, 163}, {42, 162}, {41, 161}, {9,
129}, {10, 130}, {11, 131}, {12, 132}, {13, 133}, {14, 134}, {15, 135}, {24,
144}, {25, 145}, {26, 146}, {27, 147}, {28, 148}, {29, 149}, {30, 150}, {31,
151}, {40, 160}, {67, 200}, {71, 204}, {83, 216}, {87, 220}, {99, 232}, {103,
236}, {68, 201}, {70, 203}, {84, 217}, {86, 219}, {100, 233}, {102, 235}, {69,
202}, {85, 218}, {101, 234}, {16, 136}, {55, 175}, {54, 174}, {53, 173}, {52,
172}, {51, 171}, {50, 170}, {49, 169}, {48, 168}, {17, 137}, {18, 138}, {19,
139}, {20, 140}, {21, 141}, {22, 142}, {23, 143}, {75, 208}, {79, 212}, {107,
240}, {76, 209}, {78, 211}, {77, 210}, {119, 192}, {32, 152}, {33, 153}, {34,
154}, {35, 155}, {36, 156}, {37, 157}, {38, 158}, {39, 159}, {120, 193}, {62,
132}, {63, 133}, {91, 224}, {95, 228}, {92, 225}, {94, 227}, {61, 131}, {93,
226}, {68, 128}, {71, 131}, {70, 130}, {69, 129}, {76, 136}, {77, 137}, {78,
138}, {79, 139}, {84, 144}, {85, 145}, {86, 146}, {87, 147}, {92, 152}, {93,
153}, {94, 154}, {95, 155}, {100, 160}, {101, 161}, {102, 162}, {103, 163},
{108, 168}, {109, 169}, {110, 170}, {111, 171}, {116, 176}, {117, 177}, {118,
178}, {119, 179}, {124, 184}, {125, 185}, {126, 186}, {127, 187}, {64, 134},
{72, 142}, {65, 135}, {73, 143}, {80, 150}, {81, 151}, {88, 158}, {89, 159},
{96, 166}, {97, 167}, {104, 174}, {105, 175}, {112, 185}, {114, 187}, {116,
189}, {118, 191}, {66, 136}, {71, 141}, {70, 140}, {67, 137}, {82, 152}, {83,
153}, {86, 156}, {87, 157}, {98, 168}, {99, 169}, {102, 172}, {103, 173}, {113,
186}, {117, 190}, {72, 132}, {73, 133}, {74, 134}, {75, 135}, {88, 148}, {89,
149}, {90, 150}, {91, 151}, {104, 164}, {105, 165}, {106, 166}, {107, 167},
{120, 180}, {121, 181}, {122, 182}, {123, 183}, {68, 138}, {69, 139}, {84, 154},
{85, 155}, {100, 170}, {101, 171}, {115, 188}, {111, 184}, {108, 181}, {110,
183}, {74, 144}, {75, 145}, {78, 148}, {79, 149}, {106, 176}, {107, 177}, {110,
180}, {109, 182}, {80, 140}, {81, 141}, {82, 142}, {83, 143}, {112, 172}, {113,
173}, {114, 174}, {115, 175}, {76, 146}, {77, 147}, {108, 178}, {109, 179},
{118, 128}, {119, 129}, {90, 160}, {91, 161}, {94, 164}, {95, 165}, {120, 130},
{63, 196}, {96, 156}, {97, 157}, {98, 158}, {99, 159}, {62, 195}, {92, 162},
{93, 163}, {61, 194} }>;
(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, 60)(3, 59)(4, 58)(5, 57)(6, 56)(7, 55)(8, 54)(9, 53)(10, 52)(11, 51)(12,
50)(13, 49)(14, 48)(15, 47)(16, 46)(17, 45)(18, 44)(19, 43)(20, 42)(21, 41)(22,
40)(23, 39)(24, 38)(25, 37)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(61, 178)(62,
177)(63, 176)(64, 175)(65, 174)(66, 173)(67, 172)(68, 171)(69, 170)(70, 169)(71,
168)(72, 167)(73, 166)(74, 165)(75, 164)(76, 163)(77, 162)(78, 161)(79, 160)(80,
159)(81, 158)(82, 157)(83, 156)(84, 155)(85, 154)(86, 153)(87, 152)(88, 151)(89,
150)(90, 149)(91, 148)(92, 147)(93, 146)(94, 145)(95, 144)(96, 143)(97, 142)(98,
141)(99, 140)(100, 139)(101, 138)(102, 137)(103, 136)(104, 135)(105, 134)(106,
133)(107, 132)(108, 131)(109, 130)(110, 129)(111, 128)(112, 127)(113, 126)(114,
125)(115, 124)(116, 123)(117, 122)(118, 121)(119, 180)(120, 179)(181, 191)(182,
190)(183, 189)(184, 188)(185, 187)(192, 240)(193, 239)(194, 238)(195, 237)(196,
236)(197, 235)(198, 234)(199, 233)(200, 232)(201, 231)(202, 230)(203, 229)(204,
228)(205, 227)(206, 226)(207, 225)(208, 224)(209, 223)(210, 222)(211, 221)(212,
220)(213, 219)(214, 218)(215, 217) (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, 121)(3, 61)(5, 124)(6, 64)(8, 127)(9, 67)(11, 130)(12, 70)(14, 133)(15,
73)(17, 136)(18, 76)(20, 139)(21, 79)(23, 142)(24, 82)(26, 145)(27, 85)(29,
148)(30, 88)(32, 151)(33, 91)(35, 154)(36, 94)(38, 157)(39, 97)(41, 160)(42,
100)(44, 163)(45, 103)(47, 166)(48, 106)(50, 169)(51, 109)(53, 172)(54, 112)(56,
175)(57, 115)(59, 178)(60, 118)(62, 184)(63, 134)(65, 187)(66, 137)(68, 190)(69,
140)(71, 193)(72, 143)(74, 196)(75, 146)(77, 199)(78, 149)(80, 202)(81, 152)(83,
205)(84, 155)(86, 208)(87, 158)(89, 211)(90, 161)(92, 214)(93, 164)(95, 217)(96,
167)(98, 220)(99, 170)(101, 223)(102, 173)(104, 226)(105, 176)(107, 229)(108,
179)(110, 232)(111, 122)(113, 235)(114, 125)(116, 238)(117, 128)(119, 181)(120,
131)(123, 194)(126, 197)(129, 200)(132, 203)(135, 206)(138, 209)(141, 212)(144,
215)(147, 218)(150, 221)(153, 224)(156, 227)(159, 230)(162, 233)(165, 236)(168,
239)(171, 182)(174, 185)(177, 188)(180, 191)(183, 213)(186, 216)(189, 219)(192,
222)(195, 225)(198, 228)(201, 231)(204, 234)(207, 237)(210, 240)
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)
C4[ 240, 57 ]
240
-1 121 2 60 118
-2 1 122 3 119
-3 2 123 4 120
-4 3 124 5 61
-5 4 125 6 62
-6 5 126 7 63
-7 6 127 8 64
-8 7 128 9 65
-9 66 8 129 10
-10 11 67 9 130
-11 12 68 10 131
-12 11 132 13 69
-13 12 133 14 70
-14 13 134 15 71
-15 14 135 16 72
-16 15 136 17 73
-17 16 137 18 74
-18 17 138 19 75
-19 18 139 20 76
-20 77 19 140 21
-21 22 78 20 141
-22 23 79 21 142
-23 22 143 24 80
-24 23 144 25 81
-25 24 145 26 82
-26 25 146 27 83
-27 26 147 28 84
-28 27 148 29 85
-29 28 149 30 86
-30 29 150 31 87
-31 88 30 151 32
-32 33 89 31 152
-33 34 90 32 153
-34 33 154 35 91
-35 34 155 36 92
-36 35 156 37 93
-37 36 157 38 94
-38 37 158 39 95
-39 38 159 40 96
-40 39 160 41 97
-41 40 161 42 98
-42 99 41 162 43
-43 44 100 42 163
-44 45 101 43 164
-45 44 165 46 102
-46 45 166 47 103
-47 46 167 48 104
-48 47 168 49 105
-49 48 169 50 106
-50 49 170 51 107
-51 50 171 52 108
-52 51 172 53 109
-53 110 52 173 54
-54 55 111 53 174
-55 56 112 54 175
-56 55 176 57 113
-57 56 177 58 114
-58 57 178 59 115
-59 58 179 60 116
-60 1 59 180 117
-61 121 4 194 131
-62 132 122 5 195
-63 133 123 6 196
-64 134 124 7 197
-65 198 135 125 8
-66 199 136 126 9
-67 200 137 127 10
-68 11 201 138 128
-69 12 202 139 129
-70 13 203 140 130
-71 14 204 141 131
-72 132 15 205 142
-73 143 133 16 206
-74 144 134 17 207
-75 145 135 18 208
-76 209 146 136 19
-77 210 147 137 20
-78 211 148 138 21
-79 22 212 149 139
-80 23 213 150 140
-81 24 214 151 141
-82 25 215 152 142
-83 143 26 216 153
-84 154 144 27 217
-85 155 145 28 218
-86 156 146 29 219
-87 220 157 147 30
-88 221 158 148 31
-89 222 159 149 32
-90 33 223 160 150
-91 34 224 161 151
-92 35 225 162 152
-93 36 226 163 153
-94 154 37 227 164
-95 165 155 38 228
-96 166 156 39 229
-97 167 157 40 230
-98 231 168 158 41
-99 232 169 159 42
-100 233 170 160 43
-101 44 234 171 161
-102 45 235 172 162
-103 46 236 173 163
-104 47 237 174 164
-105 165 48 238 175
-106 176 166 49 239
-107 177 167 50 240
-108 178 168 181 51
-109 179 169 182 52
-110 180 170 183 53
-111 121 171 184 54
-112 55 122 172 185
-113 56 123 173 186
-114 187 57 124 174
-115 188 58 125 175
-116 176 189 59 126
-117 177 190 60 127
-118 1 178 191 128
-119 2 179 192 129
-120 3 180 193 130
-121 1 111 181 61
-122 2 112 182 62
-123 3 113 183 63
-124 4 114 184 64
-125 5 115 185 65
-126 66 6 116 186
-127 187 67 7 117
-128 188 68 8 118
-129 189 69 9 119
-130 190 70 10 120
-131 11 191 71 61
-132 12 192 72 62
-133 13 193 73 63
-134 14 194 74 64
-135 15 195 75 65
-136 66 16 196 76
-137 77 67 17 197
-138 198 78 68 18
-139 199 79 69 19
-140 200 80 70 20
-141 201 81 71 21
-142 22 202 82 72
-143 23 203 83 73
-144 24 204 84 74
-145 25 205 85 75
-146 26 206 86 76
-147 77 27 207 87
-148 88 78 28 208
-149 209 89 79 29
-150 210 90 80 30
-151 211 91 81 31
-152 212 92 82 32
-153 33 213 93 83
-154 34 214 94 84
-155 35 215 95 85
-156 36 216 96 86
-157 37 217 97 87
-158 88 38 218 98
-159 99 89 39 219
-160 220 100 90 40
-161 221 101 91 41
-162 222 102 92 42
-163 223 103 93 43
-164 44 224 104 94
-165 45 225 105 95
-166 46 226 106 96
-167 47 227 107 97
-168 48 228 108 98
-169 99 49 229 109
-170 110 100 50 230
-171 231 111 101 51
-172 232 112 102 52
-173 233 113 103 53
-174 234 114 104 54
-175 55 235 115 105
-176 56 236 116 106
-177 57 237 117 107
-178 58 238 118 108
-179 59 239 119 109
-180 110 60 240 120
-181 121 200 222 108
-182 122 201 223 109
-183 110 123 202 224
-184 111 124 203 225
-185 112 125 204 226
-186 113 126 205 227
-187 114 127 206 228
-188 115 128 207 229
-189 116 129 208 230
-190 209 231 117 130
-191 210 232 118 131
-192 132 211 233 119
-193 133 212 234 120
-194 134 213 235 61
-195 135 214 236 62
-196 136 215 237 63
-197 137 216 238 64
-198 138 217 239 65
-199 66 139 218 240
-200 67 181 140 219
-201 220 68 182 141
-202 221 69 183 142
-203 143 222 70 184
-204 144 223 71 185
-205 145 224 72 186
-206 187 146 225 73
-207 188 147 226 74
-208 189 148 227 75
-209 190 149 228 76
-210 77 191 150 229
-211 78 192 151 230
-212 231 79 193 152
-213 232 80 194 153
-214 154 233 81 195
-215 155 234 82 196
-216 156 235 83 197
-217 198 157 236 84
-218 199 158 237 85
-219 200 159 238 86
-220 201 160 239 87
-221 88 202 161 240
-222 89 181 203 162
-223 90 182 204 163
-224 91 183 205 164
-225 165 92 184 206
-226 166 93 185 207
-227 167 94 186 208
-228 187 209 168 95
-229 188 210 169 96
-230 189 211 170 97
-231 190 212 171 98
-232 99 191 213 172
-233 100 192 214 173
-234 101 193 215 174
-235 102 194 216 175
-236 176 103 195 217
-237 177 104 196 218
-238 178 105 197 219
-239 198 220 179 106
-240 199 221 180 107
0