Graph forms
for C4 [ 240, 49 ] =
PL(LoPr_30(3,10,12,10,3),[6^20,10^12])
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On this page are computer-accessible forms for the graph C4[ 240, 49 ] =
PL(LoPr_30(3,10,12,10,3),[6^20,10^12]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {112, 123}, {110, 122}, {108, 123}, {98, 122}, {102, 126}, {98,
123}, {81, 126}, {76, 125}, {77, 126}, {79, 122}, {75, 125}, {49, 124}, {52,
122}, {44, 124}, {46, 123}, {36, 124}, {36, 125}, {34, 125}, {29, 124}, {18,
126}, {20, 121}, {13, 121}, {6, 127}, {4, 127}, {2, 127}, {4, 121}, {1, 127},
{6, 121}, {24, 152}, {65, 193}, {91, 219}, {99, 227}, {3, 130}, {75, 202}, {70,
199}, {9, 136}, {10, 139}, {21, 148}, {43, 170}, {92, 221}, {96, 225}, {8, 138},
{56, 186}, {9, 141}, {16, 148}, {104, 236}, {14, 139}, {67, 198}, {55, 178},
{19, 150}, {27, 158}, {39, 162}, {28, 154}, {63, 185}, {58, 188}, {92, 218}, {5,
130}, {64, 199}, {18, 149}, {47, 168}, {99, 228}, {106, 237}, {11, 131}, {68,
204}, {102, 238}, {13, 132}, {76, 197}, {74, 195}, {57, 176}, {33, 168}, {82,
219}, {88, 209}, {100, 237}, {26, 144}, {61, 183}, {104, 226}, {111, 229}, {10,
129}, {72, 195}, {69, 206}, {48, 187}, {53, 190}, {44, 160}, {94, 210}, {46,
163}, {73, 196}, {79, 194}, {87, 218}, {88, 213}, {100, 233}, {12, 130}, {41,
167}, {80, 222}, {101, 235}, {21, 154}, {65, 206}, {28, 147}, {11, 155}, {119,
231}, {15, 159}, {17, 129}, {31, 143}, {90, 202}, {113, 225}, {18, 131}, {118,
231}, {66, 211}, {19, 130}, {25, 136}, {26, 139}, {32, 177}, {40, 185}, {93,
204}, {71, 213}, {98, 240}, {31, 140}, {120, 235}, {78, 221}, {27, 143}, {77,
217}, {70, 210}, {63, 171}, {91, 207}, {24, 141}, {56, 173}, {43, 190}, {52,
162}, {113, 231}, {8, 159}, {76, 219}, {49, 169}, {60, 164}, {78, 214}, {45,
180}, {59, 161}, {86, 204}, {92, 198}, {30, 133}, {120, 227}, {43, 176}, {84,
207}, {38, 186}, {117, 233}, {16, 141}, {73, 212}, {42, 183}, {81, 204}, {83,
206}, {72, 214}, {91, 197}, {110, 240}, {1, 158}, {69, 218}, {64, 223}, {46,
177}, {53, 170}, {42, 138}, {67, 227}, {100, 196}, {5, 164}, {64, 225}, {25,
184}, {51, 146}, {54, 151}, {96, 193}, {27, 185}, {118, 212}, {115, 209}, {71,
229}, {48, 146}, {109, 207}, {55, 148}, {76, 239}, {17, 181}, {62, 154}, {108,
200}, {3, 166}, {59, 158}, {34, 135}, {36, 129}, {41, 140}, {45, 136}, {99,
198}, {14, 168}, {74, 236}, {31, 185}, {37, 131}, {102, 192}, {2, 165}, {9,
174}, {11, 172}, {45, 133}, {110, 198}, {66, 235}, {30, 180}, {79, 229}, {55,
156}, {58, 145}, {104, 195}, {22, 186}, {60, 144}, {28, 176}, {1, 172}, {1,
175}, {61, 147}, {2, 172}, {35, 141}, {106, 196}, {7, 168}, {56, 151}, {13,
162}, {54, 153}, {79, 224}, {23, 167}, {34, 146}, {48, 128}, {49, 129}, {84,
228}, {97, 209}, {108, 220}, {113, 193}, {9, 184}, {38, 151}, {43, 154}, {46,
159}, {50, 131}, {113, 192}, {3, 177}, {66, 240}, {22, 164}, {42, 152}, {29,
174}, {115, 192}, {3, 183}, {5, 177}, {11, 191}, {27, 175}, {38, 146}, {110,
218}, {7, 178}, {58, 143}, {20, 162}, {7, 176}, {61, 138}, {57, 142}, {17, 166},
{117, 205}, {109, 212}, {23, 173}, {29, 167}, {82, 232}, {83, 233}, {13, 182},
{14, 178}, {50, 142}, {105, 213}, {29, 160}, {87, 234}, {107, 214}, {112, 205},
{16, 174}, {18, 172}, {97, 223}, {10, 181}, {32, 159}, {81, 238}, {93, 226},
{116, 180}, {69, 132}, {89, 152}, {6, 196}, {30, 220}, {104, 170}, {69, 134},
{95, 155}, {119, 179}, {12, 201}, {118, 179}, {14, 203}, {24, 221}, {19, 213},
{77, 139}, {86, 144}, {91, 157}, {105, 175}, {45, 234}, {75, 140}, {97, 166},
{47, 231}, {39, 238}, {78, 135}, {96, 169}, {114, 187}, {20, 222}, {116, 190},
{68, 142}, {25, 211}, {39, 237}, {40, 226}, {97, 171}, {103, 173}, {36, 239},
{119, 188}, {82, 153}, {86, 157}, {88, 147}, {106, 161}, {75, 135}, {15, 194},
{33, 236}, {35, 238}, {17, 223}, {23, 217}, {33, 239}, {35, 237}, {40, 230},
{80, 158}, {103, 169}, {114, 188}, {31, 208}, {83, 156}, {108, 163}, {8, 216},
{80, 128}, {111, 191}, {26, 203}, {120, 169}, {28, 205}, {52, 229}, {87, 134},
{6, 212}, {74, 152}, {58, 232}, {49, 227}, {111, 189}, {10, 217}, {22, 197},
{24, 203}, {90, 137}, {81, 133}, {94, 138}, {53, 224}, {116, 161}, {66, 151},
{107, 190}, {30, 200}, {62, 232}, {60, 234}, {90, 140}, {15, 216}, {70, 145},
{83, 132}, {77, 149}, {93, 133}, {63, 230}, {68, 157}, {114, 171}, {8, 210},
{16, 202}, {19, 201}, {94, 132}, {103, 189}, {25, 194}, {99, 184}, {15, 211},
{119, 171}, {72, 148}, {60, 224}, {56, 228}, {20, 200}, {85, 137}, {82, 143},
{96, 189}, {55, 233}, {101, 187}, {106, 180}, {21, 202}, {57, 230}, {87, 136},
{89, 134}, {12, 236}, {62, 222}, {95, 191}, {115, 147}, {7, 230}, {112, 145},
{98, 128}, {2, 225}, {120, 155}, {118, 149}, {12, 239}, {32, 195}, {52, 215},
{85, 182}, {37, 193}, {117, 145}, {71, 163}, {89, 189}, {114, 150}, {5, 224},
{64, 165}, {59, 222}, {57, 220}, {54, 211}, {50, 215}, {95, 186}, {67, 165},
{85, 179}, {65, 166}, {73, 174}, {105, 142}, {35, 203}, {48, 216}, {94, 182},
{90, 179}, {111, 134}, {37, 206}, {68, 175}, {44, 199}, {80, 187}, {51, 223},
{84, 184}, {89, 181}, {107, 135}, {40, 197}, {116, 153}, {54, 219}, {100, 137},
{50, 220}, {78, 160}, {73, 167}, {63, 209}, {4, 235}, {38, 201}, {47, 192},
{115, 156}, {26, 234}, {61, 205}, {39, 215}, {41, 217}, {85, 165}, {109, 157},
{112, 128}, {33, 208}, {37, 215}, {107, 153}, {23, 228}, {101, 150}, {4, 240},
{59, 207}, {22, 226}, {51, 199}, {67, 182}, {84, 161}, {32, 214}, {65, 183},
{62, 200}, {42, 221}, {53, 194}, {93, 170}, {103, 144}, {71, 191}, {109, 149},
{41, 208}, {34, 216}, {72, 178}, {70, 188}, {51, 201}, {102, 156}, {86, 173},
{88, 163}, {95, 164}, {92, 160}, {117, 137}, {21, 232}, {44, 210}, {101, 155},
{47, 208}, {74, 181}, {105, 150} }>;
(II) A more general form is to represent the graph as the orbit of {112, 123}
under the group generated by the following permutations:
a: (1, 3, 9, 27, 65, 25, 31, 37, 15, 41, 50, 8, 23, 57, 94, 56, 7, 13, 38, 14,
20, 51, 26, 62, 64, 60, 21, 2, 5, 16)(4, 12, 35, 80, 17, 45, 58, 96, 53, 90, 11,
32, 73, 105, 42, 84, 63, 69, 54, 47, 52, 34, 77, 108, 44, 86, 28, 67, 22, 55)(6,
19, 24, 59, 97, 87, 82, 113, 79, 75, 18, 46, 29, 68, 61, 99, 40, 83, 66, 33, 39,
48, 10, 30, 70, 103, 43, 85, 95, 72)(36, 81, 112, 49, 93, 117, 120, 104, 100,
101, 74, 106, 114, 89, 116, 119, 111, 107, 118, 71, 78, 109, 88, 92, 91, 115,
110, 76, 102, 98)(121, 201, 203, 222, 223, 234, 232, 225, 224, 202, 172, 177,
174, 175, 183, 184, 185, 206, 211, 208, 215, 216, 217, 220, 210, 173, 176, 182,
186, 178)(122, 125, 126, 123, 124, 204, 205, 227, 226, 233, 235, 236, 237, 187,
181, 180, 188, 189, 190, 179, 191, 214, 212, 213, 221, 207, 209, 218, 219,
192)(127, 130, 141, 158, 166, 136, 143, 193, 194, 140, 131, 159, 167, 142, 138,
228, 230, 132, 151, 168, 162, 146, 139, 200, 199, 144, 154, 165, 164, 148)(128,
129, 133, 145, 169, 170, 137, 155, 195, 196, 150, 152, 161, 171, 134, 153, 231,
229, 135, 149, 163, 160, 157, 147, 198, 197, 156, 240, 239, 238) (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: (1, 2)(3, 7)(4, 6)(5, 14)(8, 21)(9, 25)(10, 22)(11, 18)(12, 33)(13, 20)(15,
16)(17, 40)(19, 47)(23, 56)(24, 53)(26, 60)(27, 64)(28, 61)(29, 54)(30, 69)(31,
51)(32, 72)(34, 75)(35, 79)(36, 76)(37, 50)(38, 41)(39, 52)(42, 43)(44, 82)(45,
87)(46, 55)(48, 90)(49, 91)(57, 65)(58, 70)(59, 67)(62, 94)(63, 97)(66, 73)(68,
96)(71, 102)(74, 104)(77, 95)(78, 107)(80, 85)(81, 111)(83, 108)(84, 99)(86,
103)(88, 115)(89, 93)(92, 116)(98, 100)(101, 118)(105, 113)(106, 110)(109,
120)(112, 117)(114, 119)(122, 237)(123, 233)(124, 219)(126, 191)(128, 137)(129,
197)(130, 168)(132, 200)(133, 134)(138, 154)(139, 164)(140, 146)(141, 194)(142,
193)(143, 199)(148, 159)(149, 155)(150, 231)(151, 167)(152, 170)(153, 160)(156,
163)(157, 169)(158, 165)(161, 198)(166, 230)(174, 211)(175, 225)(176, 183)(177,
178)(179, 187)(180, 218)(181, 226)(182, 222)(185, 223)(186, 217)(189, 204)(190,
221)(192, 213)(196, 240)(201, 208)(202, 216)(203, 224)(206, 220)(207, 227)(210,
232)(212, 235)(229, 238)
c: (2, 27)(3, 14)(4, 59)(5, 26)(6, 80)(7, 65)(8, 16)(9, 15)(10, 12)(11, 68)(13,
62)(17, 33)(18, 105)(19, 77)(21, 94)(22, 103)(23, 38)(24, 32)(28, 83)(29,
34)(30, 52)(31, 64)(35, 46)(37, 57)(39, 108)(40, 96)(41, 51)(42, 72)(43, 69)(44,
75)(45, 79)(47, 97)(48, 73)(49, 76)(53, 87)(54, 99)(55, 61)(58, 85)(63, 113)(66,
84)(67, 82)(70, 90)(71, 81)(86, 95)(88, 102)(89, 104)(91, 120)(92, 107)(93,
111)(98, 106)(100, 112)(101, 109)(110, 116)(114, 118)(121, 222)(122, 180)(123,
237)(124, 125)(126, 213)(127, 158)(128, 196)(129, 239)(130, 139)(131, 142)(132,
154)(133, 229)(134, 170)(135, 160)(136, 194)(137, 145)(138, 148)(140, 199)(141,
159)(143, 165)(144, 164)(146, 167)(147, 156)(149, 150)(151, 228)(152, 195)(153,
198)(155, 157)(161, 240)(162, 200)(163, 238)(166, 168)(169, 197)(171, 231)(172,
175)(173, 186)(174, 216)(176, 206)(177, 203)(178, 183)(179, 188)(181, 236)(182,
232)(184, 211)(185, 225)(187, 212)(189, 226)(190, 218)(191, 204)(192, 209)(193,
230)(201, 217)(202, 210)(205, 233)(207, 235)(208, 223)(214, 221)(215, 220)(219,
227)(224, 234)
d: (1, 4, 2, 6)(3, 24, 7, 53)(5, 42, 14, 43)(8, 10, 21, 22)(9, 63, 25, 97)(11,
13, 18, 20)(12, 78, 33, 107)(15, 17, 16, 40)(19, 92, 47, 116)(23, 58, 56,
70)(26, 28, 60, 61)(27, 66, 64, 73)(29, 31, 54, 51)(30, 71, 69, 102)(32, 74, 72,
104)(34, 36, 75, 76)(35, 57, 79, 65)(37, 39, 50, 52)(38, 44, 41, 82)(45, 88, 87,
115)(46, 89, 55, 93)(48, 49, 90, 91)(59, 101, 67, 118)(62, 95, 94, 77)(68, 98,
96, 100)(80, 120, 85, 109)(81, 108, 111, 83)(84, 114, 99, 119)(86, 112, 103,
117)(105, 110, 113, 106)(121, 172)(122, 193, 237, 142)(123, 189, 233, 204)(124,
140, 219, 146)(126, 200, 191, 132)(128, 169, 137, 157)(129, 202, 197, 216)(130,
221, 168, 190)(131, 162)(133, 163, 134, 156)(135, 239)(136, 209)(138, 139, 154,
164)(141, 230, 194, 166)(143, 151, 199, 167)(144, 205)(145, 173)(147, 234)(148,
226, 159, 181)(149, 222, 155, 182)(150, 198, 231, 161)(152, 178, 170, 177)(153,
201, 160, 208)(158, 235, 165, 212)(171, 184)(174, 185, 211, 223)(175, 240, 225,
196)(176, 224, 183, 203)(179, 207, 187, 227)(180, 213, 218, 192)(186, 210, 217,
232)(188, 228)(206, 238, 220, 229)(214, 236)
e: (3, 8)(4, 11)(5, 15)(6, 18)(7, 21)(9, 26)(10, 29)(12, 34)(13, 37)(14, 16)(17,
44)(19, 48)(20, 50)(22, 54)(25, 60)(33, 75)(40, 82)(47, 90)(57, 62)(58, 63)(59,
68)(65, 94)(66, 95)(67, 96)(70, 97)(71, 98)(73, 77)(74, 78)(80, 105)(81,
106)(84, 86)(85, 113)(88, 112)(89, 92)(93, 116)(99, 103)(100, 102)(104,
107)(110, 111)(115, 117)(121, 131)(122, 229)(123, 163)(124, 129)(125, 239)(126,
196)(127, 172)(128, 213)(130, 216)(132, 206)(133, 180)(134, 218)(135, 236)(136,
234)(137, 192)(138, 183)(139, 174)(140, 208)(141, 203)(142, 222)(143, 185)(144,
184)(145, 209)(146, 201)(147, 205)(148, 178)(149, 212)(150, 187)(151, 186)(152,
221)(153, 226)(154, 176)(155, 235)(156, 233)(157, 207)(158, 175)(159, 177)(160,
181)(161, 204)(162, 215)(164, 211)(165, 225)(166, 210)(167, 217)(168, 202)(169,
227)(170, 190)(171, 188)(173, 228)(179, 231)(182, 193)(189, 198)(191, 240)(194,
224)(195, 214)(197, 219)(199, 223)(200, 220)(230, 232)(237, 238)
C4[ 240, 49 ]
240
-1 158 127 172 175
-2 165 225 127 172
-3 166 177 183 130
-4 121 235 127 240
-5 177 224 130 164
-6 121 212 127 196
-7 176 178 168 230
-8 210 159 138 216
-9 136 184 141 174
-10 181 139 129 217
-11 155 191 172 131
-12 201 236 239 130
-13 121 132 182 162
-14 178 168 203 139
-15 211 159 194 216
-16 202 148 141 174
-17 166 223 181 129
-18 126 149 172 131
-19 201 213 150 130
-20 121 200 222 162
-21 154 232 202 148
-22 226 164 186 197
-23 167 173 217 228
-24 221 203 141 152
-25 211 136 194 184
-26 144 234 203 139
-27 143 158 185 175
-28 154 176 147 205
-29 167 124 160 174
-30 220 133 200 180
-31 143 140 185 208
-32 177 159 214 195
-33 168 236 239 208
-34 135 146 125 216
-35 203 237 238 141
-36 124 125 129 239
-37 193 215 206 131
-38 146 201 151 186
-39 215 237 238 162
-40 226 185 197 230
-41 167 140 217 208
-42 221 138 183 152
-43 154 176 190 170
-44 199 210 124 160
-45 133 234 136 180
-46 177 123 159 163
-47 231 168 192 208
-48 187 146 128 216
-49 124 169 227 129
-50 220 215 131 142
-51 199 146 201 223
-52 122 215 162 229
-53 190 224 170 194
-54 211 151 153 219
-55 156 178 233 148
-56 151 173 228 186
-57 176 220 142 230
-58 143 188 232 145
-59 222 158 161 207
-60 144 234 224 164
-61 147 138 183 205
-62 154 232 200 222
-63 209 171 185 230
-64 165 199 223 225
-65 166 193 183 206
-66 211 235 151 240
-67 165 198 182 227
-68 157 204 142 175
-69 132 134 206 218
-70 188 199 210 145
-71 191 213 163 229
-72 178 148 214 195
-73 167 212 174 196
-74 181 236 195 152
-75 135 125 202 140
-76 125 239 197 219
-77 126 149 139 217
-78 221 135 214 160
-79 122 224 194 229
-80 187 222 158 128
-81 133 126 204 238
-82 143 232 153 219
-83 132 156 233 206
-84 161 184 228 207
-85 165 179 137 182
-86 144 157 204 173
-87 134 234 136 218
-88 209 147 213 163
-89 134 189 181 152
-90 179 202 137 140
-91 157 207 197 219
-92 198 221 160 218
-93 133 170 204 226
-94 132 210 138 182
-95 155 191 164 186
-96 189 169 225 193
-97 209 166 223 171
-98 122 123 128 240
-99 198 227 184 228
-100 233 137 237 196
-101 187 155 235 150
-102 156 126 192 238
-103 144 189 169 173
-104 170 236 226 195
-105 213 150 142 175
-106 180 237 161 196
-107 135 190 214 153
-108 220 123 200 163
-109 157 212 149 207
-110 198 122 218 240
-111 134 189 191 229
-112 123 145 128 205
-113 231 192 225 193
-114 187 188 171 150
-115 209 156 147 192
-116 190 180 161 153
-117 145 233 137 205
-118 231 179 212 149
-119 231 188 179 171
-120 155 169 235 227
-121 13 4 6 20
-122 110 79 52 98
-123 46 112 108 98
-124 44 36 49 29
-125 34 36 75 76
-126 77 102 81 18
-127 1 2 4 6
-128 112 80 48 98
-129 36 49 17 10
-130 12 3 5 19
-131 11 37 50 18
-132 13 69 83 94
-133 45 81 93 30
-134 89 111 69 87
-135 34 78 107 75
-136 45 25 9 87
-137 100 90 117 85
-138 61 94 8 42
-139 77 14 26 10
-140 90 41 31 75
-141 24 35 16 9
-142 57 68 50 105
-143 58 27 82 31
-144 26 103 60 86
-145 112 58 70 117
-146 34 48 38 51
-147 88 115 28 61
-148 55 16 72 21
-149 77 18 118 109
-150 101 114 105 19
-151 66 56 38 54
-152 89 24 74 42
-153 82 116 107 54
-154 28 62 21 43
-155 11 101 95 120
-156 55 102 115 83
-157 68 91 86 109
-158 1 80 59 27
-159 46 15 8 32
-160 44 78 92 29
-161 59 116 84 106
-162 13 39 52 20
-163 88 46 71 108
-164 22 5 60 95
-165 67 2 85 64
-166 3 17 97 65
-167 23 29 73 41
-168 33 14 47 7
-169 103 49 96 120
-170 93 104 53 43
-171 114 63 97 119
-172 11 1 2 18
-173 23 56 103 86
-174 16 29 73 9
-175 1 68 27 105
-176 57 28 7 43
-177 46 3 5 32
-178 55 14 72 7
-179 90 85 118 119
-180 45 116 106 30
-181 89 17 74 10
-182 67 13 94 85
-183 3 61 42 65
-184 99 25 84 9
-185 27 40 63 31
-186 22 56 38 95
-187 101 80 48 114
-188 58 70 114 119
-189 89 111 103 96
-190 116 107 53 43
-191 11 111 71 95
-192 47 102 113 115
-193 113 37 96 65
-194 79 25 15 53
-195 104 72 74 32
-196 100 6 73 106
-197 22 91 40 76
-198 99 110 67 92
-199 44 70 51 64
-200 62 30 20 108
-201 12 38 51 19
-202 90 16 75 21
-203 24 35 14 26
-204 68 81 93 86
-205 112 28 61 117
-206 69 37 83 65
-207 91 59 84 109
-208 33 47 41 31
-209 88 115 63 97
-210 44 70 94 8
-211 66 25 15 54
-212 6 73 118 109
-213 88 71 105 19
-214 78 72 107 32
-215 37 39 50 52
-216 34 15 48 8
-217 77 23 41 10
-218 110 69 92 87
-219 91 82 54 76
-220 57 50 30 108
-221 78 24 92 42
-222 80 59 62 20
-223 17 51 64 97
-224 79 5 60 53
-225 2 113 96 64
-226 22 93 104 40
-227 99 67 49 120
-228 99 23 56 84
-229 111 79 71 52
-230 57 7 40 63
-231 47 113 118 119
-232 58 82 62 21
-233 55 100 83 117
-234 45 26 60 87
-235 66 101 4 120
-236 33 12 104 74
-237 100 35 39 106
-238 35 102 81 39
-239 33 12 36 76
-240 66 110 4 98
0