Graph forms
for C4 [ 273, 5 ] = PS(21,13;3)
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On this page are computer-accessible forms for the graph C4[ 273, 5 ] =
PS(21,13;3).
(I) Following is a form readable by MAGMA:
g:=Graph<273|{ {52, 53}, {130, 131}, {208, 209}, {13, 14}, {260, 263}, {104,
107}, {24, 27}, {64, 67}, {169, 170}, {180, 183}, {220, 223}, {75, 79}, {234,
238}, {233, 237}, {115, 119}, {114, 118}, {153, 157}, {154, 158}, {155, 159},
{192, 196}, {193, 197}, {194, 198}, {195, 199}, {232, 236}, {25, 28}, {259,
262}, {65, 68}, {219, 222}, {26, 29}, {258, 261}, {91, 92}, {32, 41}, {116,
125}, {114, 123}, {112, 121}, {34, 43}, {36, 45}, {38, 47}, {70, 79}, {148,
157}, {150, 159}, {192, 201}, {194, 203}, {226, 235}, {228, 237}, {230, 239},
{17, 27}, {260, 270}, {257, 267}, {256, 266}, {101, 111}, {100, 110}, {97, 107},
{96, 106}, {20, 30}, {21, 31}, {64, 74}, {65, 75}, {176, 186}, {177, 187}, {180,
190}, {181, 191}, {212, 222}, {213, 223}, {33, 42}, {117, 126}, {113, 122}, {37,
46}, {149, 158}, {193, 202}, {229, 238}, {2, 14}, {243, 255}, {242, 254}, {241,
253}, {240, 252}, {130, 142}, {129, 141}, {128, 140}, {117, 121}, {116, 120},
{83, 95}, {82, 94}, {81, 93}, {3, 15}, {36, 40}, {37, 41}, {38, 42}, {39, 43},
{48, 60}, {49, 61}, {50, 62}, {51, 63}, {80, 92}, {160, 172}, {161, 173}, {162,
174}, {163, 175}, {208, 220}, {231, 235}, {103, 106}, {181, 184}, {1, 15}, {259,
269}, {258, 268}, {241, 255}, {240, 254}, {129, 143}, {128, 142}, {99, 109},
{98, 108}, {81, 95}, {18, 28}, {19, 29}, {48, 62}, {49, 63}, {80, 94}, {160,
174}, {161, 175}, {178, 188}, {179, 189}, {35, 44}, {247, 248}, {115, 124},
{102, 105}, {182, 185}, {195, 204}, {227, 236}, {14, 30}, {257, 273}, {256,
272}, {137, 153}, {136, 152}, {135, 151}, {134, 150}, {133, 149}, {132, 148},
{131, 147}, {101, 117}, {100, 116}, {99, 115}, {98, 114}, {97, 113}, {96, 112},
{15, 31}, {138, 154}, {139, 155}, {140, 156}, {170, 186}, {171, 187}, {172,
188}, {173, 189}, {174, 190}, {175, 191}, {32, 49}, {110, 127}, {108, 125},
{106, 123}, {34, 51}, {66, 83}, {68, 85}, {70, 87}, {72, 89}, {74, 91}, {224,
241}, {226, 243}, {228, 245}, {230, 247}, {2, 16}, {239, 253}, {238, 252}, {235,
249}, {3, 17}, {6, 20}, {7, 21}, {10, 24}, {11, 25}, {42, 56}, {43, 57}, {46,
60}, {47, 61}, {79, 93}, {162, 176}, {163, 177}, {166, 180}, {167, 181}, {198,
212}, {199, 213}, {202, 216}, {203, 217}, {206, 220}, {207, 221}, {33, 50},
{109, 126}, {105, 122}, {69, 86}, {73, 90}, {225, 242}, {229, 246}, {4, 16},
{239, 251}, {238, 250}, {237, 249}, {236, 248}, {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}, {197, 209}, {198, 210}, {199, 211}, {204, 216}, {205,
217}, {206, 218}, {207, 219}, {4, 18}, {237, 251}, {236, 250}, {135, 145}, {134,
144}, {105, 127}, {103, 113}, {102, 112}, {5, 19}, {12, 26}, {44, 58}, {45, 59},
{142, 152}, {143, 153}, {164, 178}, {165, 179}, {174, 184}, {175, 185}, {196,
210}, {197, 211}, {204, 218}, {205, 219}, {224, 246}, {225, 247}, {35, 52},
{111, 120}, {107, 124}, {39, 48}, {67, 84}, {71, 80}, {227, 244}, {231, 240},
{72, 81}, {234, 243}, {133, 156}, {131, 154}, {110, 119}, {74, 83}, {76, 85},
{78, 87}, {196, 221}, {232, 241}, {66, 88}, {137, 147}, {136, 146}, {104, 114},
{67, 89}, {140, 150}, {141, 151}, {173, 183}, {1, 26}, {233, 242}, {109, 118},
{73, 82}, {77, 86}, {8, 20}, {9, 21}, {10, 22}, {11, 23}, {41, 53}, {42, 54},
{43, 55}, {76, 80}, {77, 81}, {78, 82}, {168, 180}, {169, 181}, {200, 212},
{201, 213}, {202, 214}, {203, 215}, {141, 144}, {143, 146}, {8, 22}, {138, 148},
{9, 23}, {40, 54}, {41, 55}, {68, 90}, {69, 91}, {139, 149}, {168, 182}, {200,
214}, {201, 215}, {71, 88}, {132, 155}, {75, 84}, {142, 145}, {79, 104}, {15,
38}, {93, 116}, {27, 49}, {30, 52}, {222, 244}, {223, 245}, {14, 37}, {94, 117},
{157, 182}, {28, 50}, {29, 51}, {31, 48}, {92, 115}, {223, 240}, {16, 32}, {95,
111}, {94, 110}, {93, 109}, {92, 108}, {17, 33}, {18, 34}, {19, 35}, {20, 36},
{21, 37}, {22, 38}, {23, 39}, {209, 225}, {210, 226}, {211, 227}, {212, 228},
{213, 229}, {214, 230}, {215, 231}, {216, 232}, {217, 233}, {218, 234}, {28,
45}, {30, 47}, {144, 161}, {146, 163}, {148, 165}, {150, 167}, {152, 169}, {222,
239}, {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}, {95, 105}, {85, 99}, {84, 98}, {23, 33}, {144,
166}, {145, 167}, {157, 171}, {214, 224}, {215, 225}, {16, 39}, {27, 44}, {31,
40}, {147, 164}, {151, 160}, {152, 161}, {154, 163}, {156, 165}, {209, 232},
{211, 234}, {24, 34}, {25, 35}, {146, 168}, {147, 169}, {216, 226}, {217, 227},
{220, 230}, {221, 231}, {153, 162}, {210, 233}, {88, 100}, {91, 103}, {90, 102},
{89, 101}, {156, 160}, {221, 224}, {26, 36}, {89, 103}, {88, 102}, {218, 228},
{219, 229}, {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}, {186, 203}, {188, 205}, {190, 207}, {50, 64}, {51,
65}, {185, 202}, {189, 206}, {52, 64}, {62, 72}, {63, 73}, {182, 192}, {184,
206}, {185, 207}, {187, 204}, {191, 200}, {53, 76}, {55, 78}, {188, 197}, {190,
199}, {56, 66}, {57, 67}, {60, 70}, {61, 71}, {183, 205}, {54, 77}, {189, 198},
{63, 66}, {58, 68}, {59, 69}, {183, 200}, {187, 196}, {106, 128}, {107, 129},
{108, 130}, {111, 128}, {112, 129}, {118, 132}, {127, 141}, {126, 140}, {123,
137}, {122, 136}, {119, 133}, {113, 130}, {119, 131}, {127, 139}, {126, 138},
{125, 137}, {124, 136}, {124, 138}, {125, 139}, {118, 143}, {120, 132}, {123,
135}, {122, 134}, {121, 133}, {120, 134}, {121, 135}, {5, 261}, {6, 262}, {7,
263}, {8, 264}, {9, 265}, {10, 266}, {11, 267}, {12, 268}, {13, 269}, {13, 264},
{1, 265}, {2, 266}, {3, 267}, {4, 268}, {5, 269}, {6, 270}, {7, 271}, {12, 263},
{2, 271}, {11, 262}, {1, 270}, {10, 261}, {3, 272}, {4, 273}, {8, 272}, {9,
273}, {249, 272}, {250, 273}, {235, 260}, {248, 264}, {255, 271}, {254, 270},
{253, 269}, {252, 268}, {251, 267}, {250, 266}, {249, 265}, {242, 256}, {246,
260}, {243, 257}, {244, 256}, {247, 259}, {246, 258}, {245, 257}, {244, 258},
{255, 265}, {254, 264}, {245, 259}, {248, 271}, {252, 262}, {253, 263}, {251,
261} }>;
(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: (1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144, 157, 170, 183, 196, 209,
222, 235, 248, 261)(2, 17, 36, 41, 56, 75, 80, 95, 114, 119, 134, 153, 158, 173,
192, 197, 212, 231, 236, 251, 270)(3, 20, 32, 42, 59, 71, 81, 98, 110, 120, 137,
149, 159, 176, 188, 198, 215, 227, 237, 254, 266)(4, 23, 28, 43, 62, 67, 82,
101, 106, 121, 140, 145, 160, 179, 184, 199, 218, 223, 238, 257, 262)(5, 26, 37,
44, 65, 76, 83, 104, 115, 122, 143, 154, 161, 182, 193, 200, 221, 232, 239, 260,
271)(6, 16, 33, 45, 55, 72, 84, 94, 111, 123, 133, 150, 162, 172, 189, 201, 211,
228, 240, 250, 267)(7, 19, 29, 46, 58, 68, 85, 97, 107, 124, 136, 146, 163, 175,
185, 202, 214, 224, 241, 253, 263)(8, 22, 38, 47, 61, 77, 86, 100, 116, 125,
139, 155, 164, 178, 194, 203, 217, 233, 242, 256, 272)(9, 25, 34, 48, 64, 73,
87, 103, 112, 126, 142, 151, 165, 181, 190, 204, 220, 229, 243, 259, 268)(10,
15, 30, 49, 54, 69, 88, 93, 108, 127, 132, 147, 166, 171, 186, 205, 210, 225,
244, 249, 264)(11, 18, 39, 50, 57, 78, 89, 96, 117, 128, 135, 156, 167, 174,
195, 206, 213, 234, 245, 252, 273)(12, 21, 35, 51, 60, 74, 90, 99, 113, 129,
138, 152, 168, 177, 191, 207, 216, 230, 246, 255, 269)(13, 24, 31, 52, 63, 70,
91, 102, 109, 130, 141, 148, 169, 180, 187, 208, 219, 226, 247, 258, 265) (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, 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)(236, 247)(237, 246)(238, 245)(239, 244)(240, 243)(241,
242)(249, 260)(250, 259)(251, 258)(252, 257)(253, 256)(254, 255)(262, 273)(263,
272)(264, 271)(265, 270)(266, 269)(267, 268)
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, 244,
245, 246, 247)(248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259,
260)(261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273)
C4[ 273, 5 ]
273
-1 265 15 26 270
-2 266 14 16 271
-3 267 15 17 272
-4 268 16 18 273
-5 269 17 19 261
-6 270 18 20 262
-7 271 19 21 263
-8 22 264 272 20
-9 23 265 273 21
-10 22 24 266 261
-11 23 25 267 262
-12 24 26 268 263
-13 264 14 25 269
-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
-222 244 212 239 219
-223 220 245 213 240
-224 221 246 214 241
-225 209 242 247 215
-226 210 243 235 216
-227 211 244 236 217
-228 212 245 237 218
-229 213 246 238 219
-230 220 214 247 239
-231 221 235 215 240
-232 209 236 216 241
-233 242 210 237 217
-234 243 211 238 218
-235 231 226 249 260
-236 232 248 227 250
-237 233 249 228 251
-238 234 250 229 252
-239 253 222 251 230
-240 231 254 223 252
-241 253 232 255 224
-242 254 233 256 225
-243 255 234 257 226
-244 222 256 258 227
-245 223 257 259 228
-246 224 258 260 229
-247 225 248 259 230
-248 264 236 247 271
-249 265 235 237 272
-250 266 236 238 273
-251 267 237 239 261
-252 268 238 240 262
-253 269 239 241 263
-254 242 264 270 240
-255 243 265 271 241
-256 242 244 266 272
-257 243 245 267 273
-258 244 246 268 261
-259 245 247 269 262
-260 235 246 270 263
-261 5 258 251 10
-262 11 6 259 252
-263 253 12 7 260
-264 254 13 248 8
-265 1 255 249 9
-266 2 256 250 10
-267 11 3 257 251
-268 12 4 258 252
-269 253 13 5 259
-270 1 254 6 260
-271 2 255 248 7
-272 3 256 249 8
-273 4 257 250 9
0