Graph forms
for C4 [ 240, 50 ] =
PL(KE_30(3,1,12,11,3),[10^12,12^10])
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On this page are computer-accessible forms for the graph C4[ 240, 50 ] =
PL(KE_30(3,1,12,11,3),[10^12,12^10]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {117, 125}, {112, 127}, {111, 124}, {108, 122}, {109, 122}, {102,
124}, {99, 126}, {98, 125}, {90, 122}, {93, 127}, {83, 126}, {84, 123}, {75,
126}, {74, 125}, {66, 122}, {56, 124}, {57, 126}, {54, 125}, {48, 127}, {41,
123}, {39, 124}, {33, 127}, {17, 123}, {10, 123}, {3, 121}, {5, 121}, {4, 121},
{6, 121}, {9, 137}, {92, 220}, {18, 147}, {58, 187}, {56, 185}, {51, 178}, {83,
210}, {65, 195}, {104, 234}, {108, 238}, {8, 139}, {76, 207}, {62, 189}, {14,
141}, {17, 146}, {22, 149}, {37, 166}, {104, 235}, {109, 238}, {13, 137}, {31,
155}, {99, 231}, {16, 149}, {40, 173}, {50, 183}, {88, 221}, {34, 164}, {89,
223}, {98, 228}, {106, 236}, {108, 234}, {59, 188}, {73, 206}, {68, 195}, {93,
218}, {108, 235}, {23, 159}, {30, 150}, {43, 163}, {82, 218}, {27, 146}, {70,
207}, {110, 231}, {26, 144}, {59, 177}, {33, 171}, {36, 174}, {93, 215}, {103,
237}, {21, 158}, {65, 202}, {43, 160}, {83, 216}, {100, 239}, {35, 175}, {75,
199}, {38, 170}, {100, 232}, {24, 149}, {53, 184}, {29, 144}, {42, 167}, {89,
212}, {91, 214}, {58, 180}, {77, 195}, {66, 204}, {48, 191}, {74, 197}, {67,
204}, {18, 130}, {44, 188}, {78, 222}, {81, 193}, {1, 144}, {118, 231}, {52,
165}, {28, 141}, {63, 173}, {116, 230}, {75, 217}, {73, 219}, {72, 218}, {86,
196}, {29, 142}, {43, 184}, {2, 150}, {7, 147}, {20, 128}, {35, 183}, {38, 178},
{94, 202}, {49, 164}, {69, 208}, {52, 161}, {87, 193}, {68, 211}, {11, 147},
{69, 221}, {30, 134}, {8, 145}, {16, 137}, {22, 143}, {112, 233}, {77, 215}, {9,
146}, {76, 215}, {26, 129}, {32, 187}, {42, 177}, {114, 233}, {44, 176}, {56,
164}, {53, 169}, {87, 203}, {91, 199}, {112, 236}, {3, 158}, {55, 170}, {14,
147}, {20, 137}, {79, 210}, {85, 200}, {88, 197}, {15, 145}, {33, 191}, {39,
185}, {114, 236}, {60, 163}, {61, 162}, {80, 207}, {86, 201}, {32, 128}, {60,
156}, {22, 183}, {67, 226}, {57, 152}, {53, 148}, {25, 184}, {100, 197}, {64,
226}, {82, 240}, {12, 175}, {13, 174}, {5, 161}, {9, 173}, {27, 191}, {35, 135},
{37, 129}, {47, 139}, {107, 207}, {111, 203}, {15, 170}, {64, 229}, {19, 182},
{28, 185}, {115, 214}, {23, 177}, {120, 222}, {26, 188}, {11, 172}, {71, 224},
{16, 183}, {112, 215}, {4, 172}, {63, 151}, {29, 181}, {101, 205}, {25, 176},
{62, 151}, {12, 166}, {110, 196}, {5, 174}, {21, 190}, {32, 139}, {47, 131},
{116, 216}, {51, 159}, {101, 201}, {1, 172}, {118, 219}, {2, 175}, {3, 174},
{44, 129}, {1, 175}, {74, 228}, {58, 148}, {2, 172}, {10, 164}, {31, 177}, {78,
224}, {6, 169}, {119, 216}, {55, 152}, {17, 190}, {20, 187}, {105, 198}, {59,
139}, {97, 209}, {111, 223}, {27, 170}, {61, 140}, {41, 152}, {45, 156}, {99,
210}, {7, 180}, {117, 198}, {19, 160}, {96, 211}, {103, 212}, {1, 181}, {62,
138}, {8, 188}, {10, 190}, {98, 214}, {104, 220}, {19, 166}, {46, 155}, {50,
135}, {85, 224}, {107, 222}, {9, 191}, {39, 145}, {90, 236}, {109, 219}, {14,
185}, {54, 129}, {21, 162}, {113, 198}, {2, 186}, {40, 144}, {50, 138}, {115,
203}, {15, 182}, {25, 160}, {28, 165}, {84, 237}, {102, 223}, {12, 182}, {119,
205}, {92, 230}, {96, 218}, {97, 219}, {105, 211}, {114, 200}, {36, 159}, {45,
150}, {84, 239}, {94, 229}, {102, 221}, {46, 146}, {84, 232}, {3, 190}, {16,
173}, {34, 159}, {95, 226}, {6, 184}, {120, 198}, {8, 182}, {48, 142}, {49,
143}, {81, 239}, {24, 167}, {117, 202}, {95, 224}, {74, 138}, {91, 155}, {104,
168}, {40, 233}, {93, 156}, {96, 161}, {115, 178}, {83, 145}, {95, 157}, {11,
200}, {69, 134}, {31, 220}, {79, 140}, {89, 154}, {100, 167}, {41, 237}, {65,
132}, {92, 153}, {22, 208}, {117, 179}, {73, 143}, {32, 230}, {81, 151}, {5,
194}, {7, 192}, {80, 151}, {110, 169}, {41, 225}, {78, 134}, {13, 196}, {77,
132}, {47, 230}, {64, 138}, {68, 142}, {75, 128}, {120, 179}, {86, 157}, {19,
223}, {33, 237}, {36, 232}, {45, 225}, {103, 171}, {113, 189}, {28, 209}, {46,
227}, {14, 192}, {27, 213}, {30, 208}, {82, 156}, {36, 235}, {20, 196}, {70,
150}, {63, 239}, {73, 152}, {85, 135}, {85, 134}, {78, 154}, {12, 217}, {76,
153}, {37, 240}, {23, 193}, {63, 233}, {56, 238}, {90, 141}, {106, 189}, {17,
201}, {57, 225}, {51, 235}, {58, 227}, {15, 213}, {18, 200}, {24, 194}, {21,
206}, {62, 229}, {79, 148}, {88, 131}, {91, 128}, {66, 158}, {94, 130}, {26,
199}, {67, 158}, {111, 178}, {29, 195}, {67, 157}, {59, 228}, {57, 217}, {72,
168}, {11, 234}, {49, 208}, {81, 179}, {120, 154}, {97, 131}, {106, 136}, {34,
193}, {65, 162}, {7, 227}, {10, 238}, {87, 179}, {13, 232}, {52, 209}, {49,
212}, {96, 133}, {102, 131}, {105, 140}, {38, 192}, {48, 214}, {46, 201}, {68,
163}, {101, 130}, {106, 141}, {42, 194}, {77, 165}, {115, 155}, {37, 204}, {76,
165}, {72, 161}, {60, 213}, {109, 132}, {38, 205}, {53, 222}, {95, 180}, {110,
133}, {98, 142}, {105, 133}, {70, 171}, {116, 153}, {80, 189}, {4, 234}, {97,
143}, {40, 199}, {71, 168}, {61, 210}, {90, 181}, {64, 176}, {44, 221}, {72,
186}, {118, 132}, {107, 153}, {23, 228}, {118, 133}, {71, 180}, {61, 206}, {51,
192}, {4, 240}, {79, 187}, {82, 166}, {87, 163}, {92, 168}, {69, 176}, {119,
130}, {114, 135}, {6, 240}, {52, 194}, {34, 212}, {42, 220}, {99, 149}, {18,
229}, {66, 181}, {60, 203}, {50, 197}, {43, 211}, {45, 213}, {101, 157}, {55,
206}, {89, 160}, {113, 136}, {35, 217}, {55, 205}, {54, 204}, {25, 226}, {80,
171}, {31, 227}, {70, 186}, {54, 202}, {94, 162}, {116, 136}, {71, 186}, {103,
154}, {113, 140}, {47, 209}, {24, 231}, {119, 136}, {30, 225}, {39, 216}, {86,
169}, {88, 167}, {107, 148} }>;
(II) A more general form is to represent the graph as the orbit of {117, 125}
under the group generated by the following permutations:
a: (3, 8)(4, 12)(5, 15)(6, 19)(7, 22)(9, 28)(10, 32)(11, 35)(13, 39)(14, 16)(17,
47)(18, 50)(20, 56)(21, 59)(23, 61)(24, 38)(26, 66)(27, 52)(30, 71)(31, 73)(33,
76)(34, 79)(36, 83)(40, 90)(41, 92)(42, 55)(44, 67)(45, 72)(46, 97)(48, 77)(49,
58)(51, 99)(53, 89)(57, 104)(60, 96)(63, 106)(65, 98)(69, 95)(74, 94)(75,
108)(81, 113)(84, 116)(86, 102)(87, 105)(88, 101)(91, 109)(100, 119)(103,
107)(110, 111)(115, 118)(121, 182)(122, 199)(123, 230)(124, 196)(125, 202)(126,
235)(127, 215)(128, 238)(129, 204)(130, 197)(131, 201)(132, 214)(133, 203)(134,
224)(135, 200)(136, 239)(137, 185)(138, 229)(139, 190)(140, 193)(141, 173)(142,
195)(143, 227)(144, 181)(145, 174)(146, 209)(147, 183)(148, 212)(149, 192)(150,
186)(151, 189)(152, 220)(153, 237)(154, 222)(155, 219)(156, 218)(157, 221)(158,
188)(159, 210)(160, 184)(161, 213)(162, 228)(163, 211)(164, 187)(165, 191)(166,
240)(167, 205)(168, 225)(169, 223)(170, 194)(171, 207)(172, 175)(176, 226)(177,
206)(178, 231)(179, 198)(180, 208)(216, 232)(217, 234)(233, 236) (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, 29)(3, 16)(4, 40)(5, 9)(6, 63)(7, 59)(8, 14)(10, 99)(11, 26)(12, 90)(15,
28)(17, 24)(18, 44)(19, 106)(20, 36)(21, 22)(23, 58)(25, 62)(27, 52)(30, 65)(32,
51)(33, 96)(34, 79)(35, 66)(37, 114)(38, 47)(41, 118)(42, 46)(43, 80)(45,
77)(48, 72)(49, 61)(50, 67)(53, 81)(54, 85)(55, 97)(56, 83)(57, 109)(60, 76)(68,
70)(69, 94)(71, 98)(74, 95)(75, 108)(78, 117)(82, 112)(84, 110)(86, 100)(87,
107)(88, 101)(89, 113)(91, 104)(92, 115)(102, 119)(103, 105)(111, 116)(121,
173)(122, 217)(123, 231)(124, 216)(125, 224)(126, 238)(127, 218)(128, 235)(129,
200)(130, 221)(131, 205)(132, 225)(133, 237)(134, 202)(135, 204)(136, 223)(137,
174)(138, 226)(139, 192)(140, 212)(141, 182)(142, 186)(143, 206)(144, 172)(145,
185)(146, 194)(147, 188)(148, 193)(149, 190)(150, 195)(151, 184)(152, 219)(153,
203)(154, 198)(155, 220)(156, 215)(157, 197)(158, 183)(159, 187)(160, 189)(161,
191)(162, 208)(163, 207)(164, 210)(165, 213)(166, 236)(167, 201)(168, 214)(169,
239)(170, 209)(171, 211)(175, 181)(176, 229)(177, 227)(178, 230)(179, 222)(180,
228)(196, 232)(199, 234)(233, 240)
c: (1, 2)(3, 22)(4, 35)(5, 16)(6, 50)(7, 8)(9, 52)(10, 73)(11, 12)(13, 24)(14,
15)(17, 97)(18, 19)(20, 42)(21, 49)(23, 79)(25, 64)(26, 71)(27, 28)(29, 70)(30,
66)(31, 32)(33, 77)(34, 61)(36, 99)(37, 85)(38, 39)(40, 72)(41, 109)(43, 62)(44,
95)(45, 90)(46, 47)(48, 76)(51, 83)(53, 74)(54, 78)(55, 56)(57, 108)(58, 59)(60,
106)(63, 96)(65, 103)(67, 69)(68, 80)(75, 104)(81, 105)(82, 114)(84, 118)(86,
88)(87, 113)(89, 94)(91, 92)(93, 112)(98, 107)(100, 110)(101, 102)(111,
119)(115, 116)(117, 120)(121, 183)(122, 225)(123, 219)(124, 205)(125, 222)(126,
235)(127, 215)(128, 220)(129, 224)(130, 223)(131, 201)(132, 237)(133, 239)(134,
204)(135, 240)(136, 203)(137, 194)(138, 184)(139, 227)(140, 193)(141, 213)(142,
207)(143, 190)(144, 186)(145, 192)(146, 209)(147, 182)(148, 228)(149, 174)(150,
181)(151, 211)(152, 238)(153, 214)(154, 202)(155, 230)(156, 236)(157, 221)(158,
208)(159, 210)(160, 229)(161, 173)(162, 212)(163, 189)(164, 206)(165, 191)(166,
200)(167, 196)(168, 199)(169, 197)(170, 185)(171, 195)(172, 175)(176, 226)(177,
187)(178, 216)(179, 198)(180, 188)(217, 234)(218, 233)(231, 232)
d: (1, 4, 3, 10, 34, 81, 80, 107, 79, 83, 8, 26)(2, 6, 21, 56, 23, 63, 70, 53,
61, 39, 59, 40)(5, 17, 49, 87, 62, 76, 58, 99, 15, 44, 29, 11)(7, 24, 27, 69,
68, 18, 52, 46, 22, 60, 64, 77)(9, 30, 43, 94, 28, 31, 16, 45, 25, 65, 14,
42)(12, 37, 66, 108, 36, 84, 103, 120, 113, 116, 32, 75)(13, 41, 89, 117, 106,
92, 20, 57, 19, 54, 90, 104)(33, 78, 105, 119, 47, 91, 35, 82, 67, 109, 51,
100)(38, 88, 48, 85, 96, 101, 97, 115, 50, 93, 95, 118)(55, 102, 98, 114, 72,
86, 73, 111, 74, 112, 71, 110)(121, 190, 164, 193, 151, 207, 148, 210, 145, 188,
144, 172)(122, 235, 232, 237, 154, 198, 136, 230, 128, 217, 166, 204)(123, 212,
179, 189, 153, 187, 126, 182, 129, 181, 234, 174)(124, 228, 233, 186, 169,
206)(125, 236, 168, 196, 152, 223)(127, 224, 133, 205, 131, 214, 135, 218, 157,
219, 178, 197)(130, 209, 155, 183, 156, 226, 132, 192, 167, 191, 134, 211)(137,
225, 160, 202, 141, 220)(138, 215, 180, 231, 170, 221, 142, 200, 161, 201, 143,
203)(139, 199, 175, 240, 158, 238, 159, 239, 171, 222, 140, 216)(146, 208, 163,
229, 165, 227, 149, 213, 176, 195, 147, 194)(150, 184, 162, 185, 177, 173)
e: (1, 3, 9, 29, 21, 27, 68, 61, 15, 43, 79, 8, 25, 58, 59, 64, 7, 23, 62, 14,
34, 80, 28, 49, 70, 52, 22, 2, 5, 16)(4, 13, 40, 66, 17, 48, 65, 55, 60, 105,
83, 19, 53, 32, 44, 95, 31, 74, 18, 51, 81, 106, 56, 103, 76, 97, 30, 72, 24,
35)(6, 20, 26, 67, 46, 98, 94, 38, 87, 113, 39, 89, 107, 47, 69, 71, 42, 50, 11,
36, 63, 90, 10, 33, 77, 73, 45, 96, 99, 12)(37, 86, 91, 54, 101, 115, 117, 119,
111, 120, 116, 102, 78, 92, 88, 85, 104, 100, 114, 108, 84, 112, 109, 41, 93,
118, 57, 82, 110, 75)(121, 137, 144, 158, 146, 142, 162, 170, 163, 140, 145,
160, 148, 139, 176, 180, 177, 138, 147, 159, 151, 141, 164, 171, 165, 143, 150,
161, 149, 175)(122, 123, 127, 132, 152, 156, 133, 126, 166, 169, 128, 129, 157,
155, 125, 130, 178, 179, 136, 124, 154, 153, 131, 134, 168, 167, 135, 234, 232,
233)(172, 174, 173, 181, 190, 191, 195, 206, 213, 211, 210, 182, 184, 187, 188,
226, 227, 228, 229, 192, 193, 189, 185, 212, 207, 209, 208, 186, 194, 183)(196,
199, 204, 201, 214, 202, 205, 203, 198, 216, 223, 222, 230, 221, 224, 220, 197,
200, 235, 239, 236, 238, 237, 215, 219, 225, 218, 231, 217, 240)
C4[ 240, 50 ]
240
-1 144 181 172 175
-2 150 172 175 186
-3 121 190 158 174
-4 121 234 172 240
-5 121 161 194 174
-6 121 169 184 240
-7 147 180 192 227
-8 188 145 182 139
-9 146 191 137 173
-10 123 190 238 164
-11 200 234 147 172
-12 166 182 217 175
-13 232 137 174 196
-14 147 192 141 185
-15 145 213 170 182
-16 137 149 183 173
-17 123 146 190 201
-18 200 147 130 229
-19 166 223 160 182
-20 187 137 128 196
-21 190 158 162 206
-22 143 149 183 208
-23 177 159 193 228
-24 231 167 149 194
-25 176 160 226 184
-26 144 188 199 129
-27 146 191 213 170
-28 165 209 141 185
-29 144 181 195 142
-30 134 225 150 208
-31 220 155 177 227
-32 187 128 139 230
-33 191 127 171 237
-34 212 159 193 164
-35 135 183 217 175
-36 232 235 159 174
-37 166 204 129 240
-38 178 170 192 205
-39 145 124 216 185
-40 144 199 233 173
-41 123 225 237 152
-42 220 177 167 194
-43 211 160 184 163
-44 176 188 221 129
-45 156 213 225 150
-46 155 146 201 227
-47 209 139 131 230
-48 191 214 127 142
-49 143 212 164 208
-50 135 138 183 197
-51 178 235 159 192
-52 165 209 161 194
-53 222 169 148 184
-54 125 202 204 129
-55 170 205 206 152
-56 124 238 185 164
-57 126 225 217 152
-58 187 180 148 227
-59 177 188 139 228
-60 156 213 203 163
-61 210 140 162 206
-62 189 138 151 229
-63 233 151 173 239
-64 176 138 226 229
-65 132 202 162 195
-66 122 158 181 204
-67 157 158 204 226
-68 211 195 163 142
-69 176 221 134 208
-70 171 150 207 186
-71 168 180 224 186
-72 168 161 218 186
-73 143 206 152 219
-74 125 138 228 197
-75 199 126 128 217
-76 165 215 207 153
-77 132 165 215 195
-78 154 134 222 224
-79 187 210 148 140
-80 189 171 151 207
-81 179 193 151 239
-82 166 156 218 240
-83 210 145 126 216
-84 232 123 237 239
-85 134 200 135 224
-86 157 201 169 196
-87 179 203 193 163
-88 221 167 131 197
-89 154 212 223 160
-90 122 181 236 141
-91 155 199 214 128
-92 220 168 153 230
-93 156 127 215 218
-94 202 162 130 229
-95 157 180 224 226
-96 133 211 161 218
-97 143 209 131 219
-98 125 214 228 142
-99 231 210 126 149
-100 232 167 239 197
-101 157 201 205 130
-102 221 124 223 131
-103 154 212 171 237
-104 220 168 234 235
-105 198 133 211 140
-106 189 136 236 141
-107 222 148 207 153
-108 122 234 235 238
-109 132 122 238 219
-110 231 133 169 196
-111 178 124 223 203
-112 233 236 127 215
-113 198 189 136 140
-114 200 233 135 236
-115 155 178 203 214
-116 136 216 153 230
-117 198 179 125 202
-118 132 231 133 219
-119 136 205 216 130
-120 154 198 222 179
-121 3 4 5 6
-122 66 90 108 109
-123 17 84 41 10
-124 56 111 102 39
-125 117 74 54 98
-126 99 57 83 75
-127 33 112 48 93
-128 91 20 75 32
-129 44 26 37 54
-130 101 94 18 119
-131 88 47 102 97
-132 77 118 65 109
-133 110 105 96 118
-134 78 69 30 85
-135 35 114 50 85
-136 113 116 106 119
-137 13 16 9 20
-138 50 62 74 64
-139 47 59 8 32
-140 79 113 61 105
-141 90 14 28 106
-142 68 48 29 98
-143 22 49 73 97
-144 1 26 29 40
-145 15 39 83 8
-146 46 27 17 9
-147 11 14 7 18
-148 79 58 107 53
-149 22 99 24 16
-150 45 2 70 30
-151 80 81 62 63
-152 55 57 73 41
-153 92 116 107 76
-154 78 89 103 120
-155 46 91 115 31
-156 45 60 82 93
-157 67 101 95 86
-158 66 67 3 21
-159 23 34 36 51
-160 89 25 19 43
-161 5 72 52 96
-162 61 94 21 65
-163 68 60 43 87
-164 34 56 49 10
-165 77 28 52 76
-166 12 37 82 19
-167 88 100 24 42
-168 92 71 104 72
-169 110 6 53 86
-170 55 15 27 38
-171 33 80 70 103
-172 11 1 2 4
-173 16 40 63 9
-174 13 3 36 5
-175 1 12 2 35
-176 44 25 69 64
-177 23 59 31 42
-178 111 38 115 51
-179 81 117 87 120
-180 58 71 7 95
-181 66 1 90 29
-182 12 15 8 19
-183 22 35 16 50
-184 25 6 53 43
-185 56 14 28 39
-186 2 70 71 72
-187 79 58 20 32
-188 44 26 59 8
-189 80 113 62 106
-190 3 17 10 21
-191 33 48 27 9
-192 14 38 7 51
-193 23 34 81 87
-194 24 5 52 42
-195 77 68 29 65
-196 110 13 20 86
-197 88 100 50 74
-198 113 105 117 120
-199 91 26 40 75
-200 11 114 18 85
-201 46 101 17 86
-202 94 117 54 65
-203 111 60 115 87
-204 66 67 37 54
-205 55 101 38 119
-206 55 61 73 21
-207 80 70 107 76
-208 22 69 49 30
-209 47 28 52 97
-210 99 79 61 83
-211 68 105 96 43
-212 34 89 103 49
-213 45 15 27 60
-214 91 48 115 98
-215 77 112 93 76
-216 39 83 116 119
-217 12 35 57 75
-218 82 93 72 96
-219 73 118 97 109
-220 92 104 31 42
-221 44 88 69 102
-222 78 107 53 120
-223 89 111 102 19
-224 78 71 95 85
-225 45 57 30 41
-226 67 25 95 64
-227 46 58 7 31
-228 23 59 74 98
-229 94 18 62 64
-230 47 92 116 32
-231 99 110 24 118
-232 100 13 36 84
-233 112 114 40 63
-234 11 4 104 108
-235 36 104 51 108
-236 90 112 114 106
-237 33 103 84 41
-238 56 108 10 109
-239 100 81 84 63
-240 4 37 82 6
0