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