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