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