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