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