Graph forms
for C4 [ 243, 5 ] = PS(9,27;4)
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On this page are computer-accessible forms for the graph C4[ 243, 5 ] =
PS(9,27;4).
(I) Following is a form readable by MAGMA:
g:=Graph<243|{ {161, 163}, {51, 55}, {216, 221}, {162, 164}, {27, 28}, {182,
190}, {183, 191}, {100, 110}, {101, 111}, {80, 91}, {215, 220}, {52, 56}, {54,
58}, {53, 57}, {81, 92}, {214, 219}, {212, 217}, {128, 141}, {130, 143}, {99,
109}, {128, 142}, {129, 143}, {129, 142}, {213, 218}, {66, 82}, {79, 95}, {78,
94}, {77, 93}, {76, 92}, {75, 91}, {74, 90}, {73, 89}, {72, 88}, {71, 87}, {70,
86}, {69, 85}, {68, 84}, {67, 83}, {96, 113}, {100, 117}, {98, 115}, {102, 119},
{104, 121}, {106, 123}, {108, 125}, {130, 144}, {131, 145}, {134, 148}, {135,
149}, {97, 114}, {101, 118}, {105, 122}, {131, 144}, {135, 148}, {172, 191},
{71, 82}, {79, 90}, {77, 88}, {132, 145}, {134, 147}, {171, 190}, {102, 112},
{201, 223}, {200, 222}, {103, 113}, {132, 146}, {133, 147}, {32, 55}, {99, 116},
{78, 89}, {40, 63}, {107, 124}, {133, 146}, {33, 56}, {35, 58}, {37, 60}, {39,
62}, {160, 185}, {162, 187}, {4, 30}, {199, 221}, {198, 220}, {195, 217}, {5,
31}, {104, 114}, {105, 115}, {108, 118}, {34, 57}, {76, 87}, {72, 83}, {38, 61},
{161, 186}, {1, 29}, {2, 30}, {3, 31}, {73, 84}, {75, 86}, {160, 189}, {2, 28},
{197, 219}, {196, 218}, {3, 29}, {106, 116}, {107, 117}, {32, 63}, {74, 85},
{36, 59}, {103, 120}, {192, 224}, {211, 243}, {210, 242}, {209, 241}, {208,
240}, {207, 239}, {206, 238}, {205, 237}, {204, 236}, {203, 235}, {202, 234},
{201, 233}, {200, 232}, {199, 231}, {198, 230}, {197, 229}, {196, 228}, {195,
227}, {194, 226}, {193, 225}, {29, 60}, {31, 62}, {30, 61}, {139, 168}, {143,
172}, {147, 176}, {151, 180}, {155, 184}, {159, 188}, {4, 32}, {5, 33}, {6, 34},
{7, 35}, {12, 40}, {13, 41}, {14, 42}, {15, 43}, {20, 48}, {21, 49}, {22, 50},
{23, 51}, {82, 119}, {90, 127}, {88, 125}, {140, 169}, {142, 171}, {148, 177},
{150, 179}, {156, 185}, {158, 187}, {6, 32}, {65, 103}, {64, 102}, {7, 33}, {14,
40}, {15, 41}, {22, 48}, {23, 49}, {28, 59}, {89, 126}, {141, 170}, {143, 168},
{149, 178}, {151, 176}, {157, 186}, {159, 184}, {138, 163}, {140, 165}, {142,
167}, {152, 177}, {154, 179}, {156, 181}, {158, 183}, {8, 34}, {207, 229}, {206,
228}, {203, 225}, {202, 224}, {70, 108}, {67, 105}, {66, 104}, {9, 35}, {12,
38}, {13, 39}, {24, 50}, {25, 51}, {64, 107}, {87, 124}, {83, 120}, {141, 166},
{153, 178}, {157, 182}, {8, 36}, {83, 127}, {82, 126}, {9, 37}, {10, 38}, {11,
39}, {24, 52}, {25, 53}, {26, 54}, {65, 108}, {86, 123}, {84, 121}, {136, 165},
{138, 167}, {152, 181}, {154, 183}, {10, 36}, {205, 227}, {204, 226}, {69, 107},
{68, 106}, {11, 37}, {26, 52}, {27, 53}, {85, 122}, {95, 112}, {137, 166}, {139,
164}, {153, 182}, {155, 180}, {80, 96}, {81, 97}, {92, 109}, {194, 243}, {192,
241}, {94, 111}, {93, 110}, {193, 242}, {136, 188}, {137, 189}, {208, 230},
{216, 238}, {209, 231}, {1, 54}, {144, 169}, {146, 171}, {148, 173}, {150, 175},
{16, 42}, {215, 237}, {214, 236}, {211, 233}, {210, 232}, {17, 43}, {20, 46},
{21, 47}, {145, 170}, {149, 174}, {16, 44}, {17, 45}, {18, 46}, {19, 47}, {144,
173}, {146, 175}, {18, 44}, {213, 235}, {212, 234}, {19, 45}, {145, 174}, {147,
172}, {30, 80}, {31, 81}, {191, 240}, {190, 239}, {28, 78}, {29, 79}, {55, 98},
{63, 106}, {61, 104}, {62, 105}, {58, 96}, {63, 101}, {62, 100}, {59, 97}, {56,
99}, {60, 103}, {57, 100}, {59, 102}, {60, 98}, {61, 99}, {58, 101}, {190, 222},
{191, 223}, {33, 64}, {49, 80}, {47, 78}, {45, 76}, {35, 66}, {37, 68}, {39,
70}, {41, 72}, {43, 74}, {34, 65}, {50, 81}, {46, 77}, {38, 69}, {42, 73}, {164,
199}, {168, 203}, {172, 207}, {176, 211}, {180, 215}, {163, 198}, {169, 204},
{171, 206}, {177, 212}, {179, 214}, {56, 94}, {57, 95}, {36, 67}, {44, 75},
{170, 205}, {178, 213}, {41, 64}, {47, 70}, {45, 68}, {43, 66}, {55, 93}, {42,
65}, {46, 69}, {165, 200}, {189, 208}, {167, 202}, {173, 192}, {175, 194}, {181,
216}, {40, 71}, {44, 67}, {166, 201}, {174, 193}, {163, 209}, {166, 212}, {167,
213}, {170, 216}, {176, 195}, {188, 207}, {184, 203}, {180, 199}, {177, 196},
{187, 206}, {185, 204}, {179, 198}, {164, 210}, {165, 211}, {48, 71}, {186,
205}, {178, 197}, {184, 192}, {189, 197}, {188, 196}, {187, 195}, {186, 194},
{185, 193}, {49, 72}, {53, 76}, {51, 74}, {50, 73}, {54, 77}, {173, 208}, {183,
202}, {175, 210}, {181, 200}, {168, 214}, {169, 215}, {48, 79}, {52, 75}, {174,
209}, {182, 201}, {24, 220}, {25, 221}, {26, 222}, {27, 223}, {21, 217}, {22,
218}, {23, 219}, {8, 217}, {10, 219}, {12, 221}, {14, 223}, {9, 218}, {13, 222},
{84, 128}, {87, 131}, {86, 130}, {85, 129}, {11, 220}, {119, 160}, {120, 160},
{121, 161}, {122, 162}, {120, 161}, {91, 128}, {95, 132}, {121, 162}, {88, 132},
{91, 135}, {90, 134}, {89, 133}, {92, 129}, {94, 131}, {93, 130}, {1, 224}, {3,
226}, {5, 228}, {7, 230}, {9, 232}, {11, 234}, {13, 236}, {15, 238}, {17, 240},
{19, 242}, {2, 225}, {6, 229}, {10, 233}, {14, 237}, {18, 241}, {96, 133}, {98,
135}, {4, 227}, {97, 134}, {12, 235}, {20, 243}, {112, 152}, {113, 153}, {114,
154}, {115, 155}, {116, 156}, {117, 157}, {118, 158}, {119, 159}, {112, 153},
{114, 155}, {116, 157}, {118, 159}, {113, 154}, {117, 158}, {1, 237}, {2, 238},
{3, 239}, {8, 231}, {15, 224}, {115, 156}, {16, 225}, {18, 227}, {20, 229}, {22,
231}, {24, 233}, {26, 235}, {122, 136}, {123, 137}, {126, 140}, {127, 141}, {17,
226}, {21, 230}, {25, 234}, {123, 136}, {127, 140}, {4, 240}, {5, 241}, {6,
242}, {7, 243}, {124, 137}, {126, 139}, {124, 138}, {125, 139}, {19, 228}, {27,
236}, {111, 152}, {125, 138}, {109, 149}, {110, 150}, {111, 151}, {110, 151},
{109, 150}, {16, 239}, {23, 232} }>;
(II) A more general form is to represent the graph as the orbit of {161, 163}
under the group generated by the following permutations:
a: (2, 27)(3, 26)(4, 25)(5, 24)(6, 23)(7, 22)(8, 21)(9, 20)(10, 19)(11, 18)(12,
17)(13, 16)(14, 15)(29, 54)(30, 53)(31, 52)(32, 51)(33, 50)(34, 49)(35, 48)(36,
47)(37, 46)(38, 45)(39, 44)(40, 43)(41, 42)(56, 81)(57, 80)(58, 79)(59, 78)(60,
77)(61, 76)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)(83, 108)(84,
107)(85, 106)(86, 105)(87, 104)(88, 103)(89, 102)(90, 101)(91, 100)(92, 99)(93,
98)(94, 97)(95, 96)(110, 135)(111, 134)(112, 133)(113, 132)(114, 131)(115,
130)(116, 129)(117, 128)(118, 127)(119, 126)(120, 125)(121, 124)(122, 123)(137,
162)(138, 161)(139, 160)(140, 159)(141, 158)(142, 157)(143, 156)(144, 155)(145,
154)(146, 153)(147, 152)(148, 151)(149, 150)(164, 189)(165, 188)(166, 187)(167,
186)(168, 185)(169, 184)(170, 183)(171, 182)(172, 181)(173, 180)(174, 179)(175,
178)(176, 177)(191, 216)(192, 215)(193, 214)(194, 213)(195, 212)(196, 211)(197,
210)(198, 209)(199, 208)(200, 207)(201, 206)(202, 205)(203, 204)(218, 243)(219,
242)(220, 241)(221, 240)(222, 239)(223, 238)(224, 237)(225, 236)(226, 235)(227,
234)(228, 233)(229, 232)(230, 231) (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, 28, 55, 82, 109, 136, 163, 190, 217)(2, 51, 71, 99, 122, 138, 182, 195,
224, 27, 32, 66, 92, 123, 161, 171, 212, 237)(3, 47, 60, 89, 135, 140, 174, 200,
231, 26, 36, 77, 102, 110, 159, 179, 207, 230)(4, 43, 76, 106, 121, 142, 166,
205, 238, 25, 40, 61, 85, 124, 157, 187, 202, 223)(5, 39, 65, 96, 134, 144, 185,
210, 218, 24, 44, 72, 95, 111, 155, 168, 197, 243)(6, 35, 81, 86, 120, 146, 177,
215, 225, 23, 48, 56, 105, 125, 153, 176, 192, 236)(7, 31, 70, 103, 133, 148,
169, 193, 232, 22, 52, 67, 88, 112, 151, 184, 214, 229)(8, 54, 59, 93, 119, 150,
188, 198, 239, 21, 29, 78, 98, 126, 149, 165, 209, 222)(9, 50, 75, 83, 132, 152,
180, 203, 219, 20, 33, 62, 108, 113, 147, 173, 204, 242)(10, 46, 64, 100, 118,
154, 172, 208, 226, 19, 37, 73, 91, 127, 145, 181, 199, 235)(11, 42, 80, 90,
131, 156, 164, 213, 233, 18, 41, 57, 101, 114, 143, 189, 194, 228)(12, 38, 69,
107, 117, 158, 183, 191, 240, 17, 45, 68, 84, 128, 141, 170, 216, 221)(13, 34,
58, 97, 130, 160, 175, 196, 220, 16, 49, 79, 94, 115, 139, 178, 211, 241)(14,
30, 74, 87, 116, 162, 167, 201, 227, 15, 53, 63, 104, 129, 137, 186, 206,
234)
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, 235, 236, 237, 238, 239, 240, 241, 242, 243)
C4[ 243, 5 ]
243
-1 224 237 29 54
-2 225 28 238 30
-3 226 29 239 31
-4 227 30 240 32
-5 33 228 31 241
-6 242 34 229 32
-7 33 243 35 230
-8 231 34 36 217
-9 232 35 37 218
-10 233 36 38 219
-11 220 234 37 39
-12 221 235 38 40
-13 222 236 39 41
-14 223 237 40 42
-15 224 238 41 43
-16 44 225 239 42
-17 45 226 240 43
-18 44 46 227 241
-19 242 45 47 228
-20 243 46 48 229
-21 47 49 217 230
-22 231 48 50 218
-23 232 49 51 219
-24 220 233 50 52
-25 221 234 51 53
-26 222 235 52 54
-27 223 236 28 53
-28 78 2 59 27
-29 1 79 3 60
-30 2 80 4 61
-31 3 81 5 62
-32 55 4 6 63
-33 56 5 7 64
-34 57 6 8 65
-35 66 58 7 9
-36 67 59 8 10
-37 11 68 60 9
-38 12 69 61 10
-39 11 13 70 62
-40 12 14 71 63
-41 13 15 72 64
-42 14 16 73 65
-43 66 15 17 74
-44 67 16 18 75
-45 68 17 19 76
-46 77 69 18 20
-47 78 70 19 21
-48 22 79 71 20
-49 23 80 72 21
-50 22 24 81 73
-51 55 23 25 74
-52 56 24 26 75
-53 57 25 27 76
-54 77 1 58 26
-55 93 51 32 98
-56 33 99 94 52
-57 34 100 95 53
-58 35 101 96 54
-59 36 102 28 97
-60 37 103 29 98
-61 99 38 104 30
-62 100 39 105 31
-63 101 40 106 32
-64 33 102 41 107
-65 34 103 42 108
-66 35 82 104 43
-67 44 36 83 105
-68 45 37 84 106
-69 46 38 85 107
-70 47 39 86 108
-71 48 82 40 87
-72 88 49 83 41
-73 89 50 84 42
-74 90 51 85 43
-75 44 91 52 86
-76 45 92 53 87
-77 88 46 93 54
-78 89 47 28 94
-79 90 48 29 95
-80 91 49 30 96
-81 92 50 31 97
-82 66 71 126 119
-83 67 72 127 120
-84 121 68 73 128
-85 122 69 74 129
-86 123 70 75 130
-87 124 71 76 131
-88 77 132 125 72
-89 78 133 126 73
-90 79 134 127 74
-91 80 135 128 75
-92 81 129 76 109
-93 55 77 110 130
-94 56 78 111 131
-95 132 57 79 112
-96 133 58 80 113
-97 134 59 81 114
-98 55 135 60 115
-99 56 61 116 109
-100 110 57 62 117
-101 111 58 63 118
-102 112 59 64 119
-103 113 60 65 120
-104 66 121 114 61
-105 67 122 115 62
-106 68 123 116 63
-107 69 124 117 64
-108 70 125 118 65
-109 99 92 149 150
-110 100 93 150 151
-111 101 94 151 152
-112 102 95 152 153
-113 154 103 96 153
-114 154 155 104 97
-115 155 156 105 98
-116 99 156 157 106
-117 100 157 158 107
-118 101 158 159 108
-119 102 82 159 160
-120 103 83 160 161
-121 104 84 161 162
-122 136 105 85 162
-123 136 137 106 86
-124 137 138 107 87
-125 88 138 139 108
-126 89 82 139 140
-127 90 83 140 141
-128 91 84 141 142
-129 143 92 85 142
-130 143 144 93 86
-131 144 145 94 87
-132 88 145 146 95
-133 89 146 147 96
-134 90 147 148 97
-135 91 148 149 98
-136 165 122 188 123
-137 166 123 189 124
-138 167 124 125 163
-139 168 125 126 164
-140 165 169 126 127
-141 166 170 127 128
-142 167 171 128 129
-143 168 172 129 130
-144 169 173 130 131
-145 132 170 174 131
-146 132 133 171 175
-147 176 133 134 172
-148 177 134 135 173
-149 178 135 174 109
-150 110 179 109 175
-151 110 176 111 180
-152 111 177 112 181
-153 112 178 113 182
-154 113 179 114 183
-155 114 180 115 184
-156 115 181 116 185
-157 116 182 117 186
-158 187 117 183 118
-159 188 118 184 119
-160 189 119 185 120
-161 121 163 120 186
-162 121 187 122 164
-163 198 209 138 161
-164 199 210 139 162
-165 200 211 136 140
-166 201 212 137 141
-167 202 213 138 142
-168 143 203 214 139
-169 144 204 215 140
-170 145 205 216 141
-171 146 190 206 142
-172 143 147 191 207
-173 144 148 192 208
-174 209 145 149 193
-175 210 146 150 194
-176 211 147 151 195
-177 212 148 152 196
-178 213 149 153 197
-179 154 198 214 150
-180 155 199 215 151
-181 156 200 216 152
-182 157 190 201 153
-183 154 158 191 202
-184 155 159 192 203
-185 156 160 193 204
-186 157 161 194 205
-187 158 162 195 206
-188 136 159 196 207
-189 137 160 197 208
-190 222 171 182 239
-191 223 172 183 240
-192 224 173 184 241
-193 242 225 174 185
-194 243 226 175 186
-195 176 187 227 217
-196 177 188 228 218
-197 178 189 229 219
-198 220 179 163 230
-199 231 221 180 164
-200 165 232 222 181
-201 166 233 223 182
-202 167 234 224 183
-203 168 235 225 184
-204 169 236 226 185
-205 170 237 227 186
-206 187 171 238 228
-207 188 172 239 229
-208 189 173 240 230
-209 231 163 174 241
-210 242 232 164 175
-211 165 176 243 233
-212 166 177 234 217
-213 167 178 235 218
-214 168 179 236 219
-215 220 169 180 237
-216 221 170 181 238
-217 212 8 195 21
-218 22 213 9 196
-219 23 214 10 197
-220 11 198 24 215
-221 12 199 25 216
-222 13 200 190 26
-223 14 201 191 27
-224 1 15 202 192
-225 2 16 203 193
-226 3 17 204 194
-227 4 18 205 195
-228 5 19 206 196
-229 6 20 207 197
-230 198 7 21 208
-231 22 209 199 8
-232 23 210 200 9
-233 24 211 201 10
-234 11 25 212 202
-235 12 26 213 203
-236 13 27 214 204
-237 1 14 215 205
-238 2 15 216 206
-239 3 190 16 207
-240 4 191 17 208
-241 209 5 192 18
-242 210 6 193 19
-243 211 7 194 20
0