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