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