Graph forms
for C4 [ 279, 3 ] = PS(9,31;5)
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On this page are computer-accessible forms for the graph C4[ 279, 3 ] =
PS(9,31;5).
(I) Following is a form readable by MAGMA:
g:=Graph<279|{ {124, 125}, {217, 218}, {58, 63}, {248, 253}, {152, 157}, {154,
159}, {88, 94}, {89, 95}, {184, 190}, {185, 191}, {153, 158}, {182, 188}, {183,
189}, {151, 156}, {247, 252}, {244, 249}, {246, 251}, {181, 187}, {245, 250},
{70, 95}, {162, 187}, {164, 189}, {166, 191}, {37, 63}, {229, 255}, {228, 254},
{225, 251}, {224, 250}, {132, 158}, {133, 159}, {69, 94}, {165, 190}, {96, 126},
{227, 253}, {226, 252}, {97, 127}, {130, 156}, {131, 157}, {192, 222}, {193,
223}, {163, 188}, {1, 33}, {216, 248}, {215, 247}, {95, 127}, {94, 126}, {2,
34}, {3, 35}, {4, 36}, {5, 37}, {6, 38}, {7, 39}, {8, 40}, {9, 41}, {10, 42},
{11, 43}, {12, 44}, {13, 45}, {14, 46}, {15, 47}, {16, 48}, {17, 49}, {18, 50},
{19, 51}, {20, 52}, {21, 53}, {22, 54}, {23, 55}, {24, 56}, {25, 57}, {26, 58},
{27, 59}, {28, 60}, {29, 61}, {30, 62}, {192, 224}, {193, 225}, {194, 226},
{195, 227}, {196, 228}, {197, 229}, {198, 230}, {199, 231}, {200, 232}, {201,
233}, {202, 234}, {203, 235}, {204, 236}, {205, 237}, {206, 238}, {207, 239},
{208, 240}, {209, 241}, {210, 242}, {211, 243}, {212, 244}, {213, 245}, {214,
246}, {2, 32}, {215, 245}, {95, 125}, {3, 33}, {6, 36}, {7, 37}, {10, 40}, {11,
41}, {14, 44}, {15, 45}, {18, 48}, {19, 49}, {22, 52}, {23, 53}, {26, 56}, {27,
57}, {30, 60}, {31, 61}, {194, 224}, {195, 225}, {198, 228}, {199, 229}, {202,
232}, {203, 233}, {206, 236}, {207, 237}, {210, 240}, {211, 241}, {214, 244},
{128, 164}, {219, 255}, {218, 254}, {129, 165}, {130, 166}, {131, 167}, {136,
172}, {137, 173}, {138, 174}, {139, 175}, {144, 180}, {145, 181}, {146, 182},
{147, 183}, {64, 101}, {82, 119}, {80, 117}, {74, 111}, {72, 109}, {66, 103},
{4, 34}, {223, 249}, {5, 35}, {12, 42}, {13, 43}, {20, 50}, {21, 51}, {28, 58},
{29, 59}, {134, 160}, {135, 161}, {142, 168}, {143, 169}, {150, 176}, {151,
177}, {196, 226}, {197, 227}, {204, 234}, {205, 235}, {212, 242}, {213, 243},
{65, 102}, {87, 112}, {81, 118}, {79, 104}, {73, 110}, {71, 96}, {72, 97}, {92,
117}, {90, 115}, {88, 113}, {78, 103}, {76, 101}, {74, 99}, {136, 162}, {137,
163}, {140, 166}, {141, 167}, {152, 178}, {153, 179}, {67, 104}, {93, 118}, {89,
114}, {87, 124}, {83, 120}, {77, 102}, {73, 98}, {71, 108}, {132, 168}, {133,
169}, {134, 170}, {135, 171}, {148, 184}, {149, 185}, {150, 186}, {68, 105},
{86, 123}, {84, 121}, {70, 107}, {8, 38}, {217, 247}, {216, 246}, {9, 39}, {24,
54}, {25, 55}, {138, 164}, {139, 165}, {154, 180}, {155, 181}, {200, 230}, {201,
231}, {69, 106}, {91, 116}, {85, 122}, {75, 100}, {64, 120}, {68, 124}, {67,
123}, {66, 122}, {65, 121}, {80, 105}, {86, 111}, {84, 109}, {82, 107}, {128,
185}, {90, 96}, {91, 97}, {144, 170}, {145, 171}, {148, 174}, {149, 175}, {75,
112}, {85, 110}, {81, 106}, {79, 116}, {129, 186}, {155, 160}, {140, 176}, {141,
177}, {142, 178}, {143, 179}, {76, 113}, {78, 115}, {16, 46}, {93, 99}, {92,
98}, {17, 47}, {146, 172}, {147, 173}, {208, 238}, {209, 239}, {1, 62}, {83,
108}, {77, 114}, {31, 32}, {187, 248}, {63, 119}, {156, 212}, {157, 213}, {158,
214}, {159, 215}, {63, 100}, {159, 196}, {156, 193}, {158, 195}, {157, 194},
{187, 219}, {188, 220}, {189, 221}, {190, 222}, {191, 223}, {190, 220}, {191,
221}, {32, 68}, {57, 93}, {56, 92}, {51, 87}, {33, 69}, {34, 70}, {35, 71}, {40,
76}, {41, 77}, {42, 78}, {43, 79}, {48, 84}, {49, 85}, {50, 86}, {160, 197},
{162, 199}, {168, 205}, {170, 207}, {176, 213}, {178, 215}, {38, 64}, {62, 88},
{55, 81}, {54, 80}, {39, 65}, {46, 72}, {47, 73}, {188, 218}, {189, 219}, {161,
198}, {167, 192}, {169, 206}, {175, 200}, {177, 214}, {183, 208}, {168, 193},
{170, 195}, {172, 197}, {174, 199}, {184, 209}, {186, 211}, {40, 66}, {61, 87},
{60, 86}, {57, 83}, {56, 82}, {41, 67}, {44, 70}, {45, 71}, {163, 200}, {167,
204}, {169, 194}, {173, 198}, {179, 216}, {185, 210}, {36, 72}, {55, 91}, {54,
90}, {53, 89}, {52, 88}, {37, 73}, {38, 74}, {39, 75}, {164, 201}, {166, 203},
{180, 217}, {42, 68}, {59, 85}, {58, 84}, {43, 69}, {165, 202}, {171, 196},
{160, 216}, {161, 217}, {32, 89}, {34, 91}, {36, 93}, {176, 201}, {178, 203},
{180, 205}, {182, 207}, {48, 74}, {53, 79}, {52, 78}, {49, 75}, {186, 192}, {33,
90}, {59, 64}, {171, 208}, {175, 212}, {177, 202}, {181, 206}, {44, 80}, {45,
81}, {46, 82}, {47, 83}, {60, 65}, {62, 67}, {172, 209}, {174, 211}, {50, 76},
{51, 77}, {35, 92}, {61, 66}, {173, 210}, {179, 204}, {94, 155}, {127, 184},
{126, 183}, {125, 182}, {125, 161}, {126, 162}, {127, 163}, {96, 128}, {112,
144}, {111, 143}, {110, 142}, {109, 141}, {108, 140}, {107, 139}, {106, 138},
{105, 137}, {104, 136}, {103, 135}, {102, 134}, {101, 133}, {100, 132}, {99,
131}, {98, 130}, {97, 129}, {113, 145}, {114, 146}, {115, 147}, {116, 148},
{117, 149}, {118, 150}, {119, 151}, {120, 152}, {121, 153}, {122, 154}, {123,
155}, {27, 250}, {29, 252}, {31, 254}, {98, 128}, {111, 141}, {110, 140}, {107,
137}, {106, 136}, {103, 133}, {102, 132}, {99, 129}, {114, 144}, {115, 145},
{118, 148}, {119, 149}, {122, 152}, {123, 153}, {26, 249}, {30, 253}, {100,
130}, {109, 139}, {108, 138}, {101, 131}, {116, 146}, {117, 147}, {124, 154},
{28, 251}, {104, 134}, {105, 135}, {120, 150}, {121, 151}, {8, 250}, {9, 251},
{12, 254}, {13, 255}, {10, 252}, {11, 253}, {1, 255}, {113, 143}, {112, 142},
{7, 249}, {2, 256}, {3, 257}, {6, 260}, {7, 261}, {10, 264}, {11, 265}, {14,
268}, {15, 269}, {18, 272}, {19, 273}, {22, 276}, {23, 277}, {4, 258}, {5, 259},
{12, 266}, {13, 267}, {20, 274}, {21, 275}, {8, 262}, {9, 263}, {14, 256}, {15,
257}, {24, 278}, {25, 279}, {30, 272}, {31, 273}, {2, 275}, {4, 277}, {6, 279},
{16, 258}, {17, 259}, {20, 262}, {21, 263}, {24, 266}, {25, 267}, {28, 270},
{29, 271}, {1, 274}, {5, 278}, {18, 260}, {19, 261}, {26, 268}, {27, 269}, {3,
276}, {16, 270}, {17, 271}, {22, 264}, {23, 265}, {218, 275}, {222, 279}, {220,
277}, {221, 278}, {219, 276}, {220, 256}, {223, 259}, {222, 258}, {221, 257},
{224, 260}, {243, 279}, {242, 278}, {241, 277}, {240, 276}, {235, 271}, {234,
270}, {233, 269}, {232, 268}, {227, 263}, {226, 262}, {225, 261}, {230, 256},
{247, 273}, {246, 272}, {239, 265}, {238, 264}, {231, 257}, {232, 258}, {248,
274}, {237, 263}, {236, 262}, {233, 259}, {228, 264}, {231, 267}, {230, 266},
{229, 265}, {234, 260}, {235, 261}, {240, 266}, {245, 271}, {244, 270}, {241,
267}, {236, 272}, {239, 275}, {238, 274}, {237, 273}, {242, 268}, {243, 269}
}>;
(II) A more general form is to represent the graph as the orbit of {124, 125}
under the group generated by the following permutations:
a: (2, 31)(3, 30)(4, 29)(5, 28)(6, 27)(7, 26)(8, 25)(9, 24)(10, 23)(11, 22)(12,
21)(13, 20)(14, 19)(15, 18)(16, 17)(33, 62)(34, 61)(35, 60)(36, 59)(37, 58)(38,
57)(39, 56)(40, 55)(41, 54)(42, 53)(43, 52)(44, 51)(45, 50)(46, 49)(47, 48)(64,
93)(65, 92)(66, 91)(67, 90)(68, 89)(69, 88)(70, 87)(71, 86)(72, 85)(73, 84)(74,
83)(75, 82)(76, 81)(77, 80)(78, 79)(95, 124)(96, 123)(97, 122)(98, 121)(99,
120)(100, 119)(101, 118)(102, 117)(103, 116)(104, 115)(105, 114)(106, 113)(107,
112)(108, 111)(109, 110)(126, 155)(127, 154)(128, 153)(129, 152)(130, 151)(131,
150)(132, 149)(133, 148)(134, 147)(135, 146)(136, 145)(137, 144)(138, 143)(139,
142)(140, 141)(157, 186)(158, 185)(159, 184)(160, 183)(161, 182)(162, 181)(163,
180)(164, 179)(165, 178)(166, 177)(167, 176)(168, 175)(169, 174)(170, 173)(171,
172)(188, 217)(189, 216)(190, 215)(191, 214)(192, 213)(193, 212)(194, 211)(195,
210)(196, 209)(197, 208)(198, 207)(199, 206)(200, 205)(201, 204)(202, 203)(219,
248)(220, 247)(221, 246)(222, 245)(223, 244)(224, 243)(225, 242)(226, 241)(227,
240)(228, 239)(229, 238)(230, 237)(231, 236)(232, 235)(233, 234)(250, 279)(251,
278)(252, 277)(253, 276)(254, 275)(255, 274)(256, 273)(257, 272)(258, 271)(259,
270)(260, 269)(261, 268)(262, 267)(263, 266)(264, 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: (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, 274, 275, 276,
277, 278, 279)
c: (1, 32, 63, 94, 125, 156, 187, 218, 249)(2, 37, 88, 95, 130, 181, 188, 223,
274)(3, 42, 82, 96, 135, 175, 189, 228, 268)(4, 47, 76, 97, 140, 169, 190, 233,
262)(5, 52, 70, 98, 145, 163, 191, 238, 256)(6, 57, 64, 99, 150, 157, 192, 243,
250)(7, 62, 89, 100, 155, 182, 193, 248, 275)(8, 36, 83, 101, 129, 176, 194,
222, 269)(9, 41, 77, 102, 134, 170, 195, 227, 263)(10, 46, 71, 103, 139, 164,
196, 232, 257)(11, 51, 65, 104, 144, 158, 197, 237, 251)(12, 56, 90, 105, 149,
183, 198, 242, 276)(13, 61, 84, 106, 154, 177, 199, 247, 270)(14, 35, 78, 107,
128, 171, 200, 221, 264)(15, 40, 72, 108, 133, 165, 201, 226, 258)(16, 45, 66,
109, 138, 159, 202, 231, 252)(17, 50, 91, 110, 143, 184, 203, 236, 277)(18, 55,
85, 111, 148, 178, 204, 241, 271)(19, 60, 79, 112, 153, 172, 205, 246, 265)(20,
34, 73, 113, 127, 166, 206, 220, 259)(21, 39, 67, 114, 132, 160, 207, 225,
253)(22, 44, 92, 115, 137, 185, 208, 230, 278)(23, 49, 86, 116, 142, 179, 209,
235, 272)(24, 54, 80, 117, 147, 173, 210, 240, 266)(25, 59, 74, 118, 152, 167,
211, 245, 260)(26, 33, 68, 119, 126, 161, 212, 219, 254)(27, 38, 93, 120, 131,
186, 213, 224, 279)(28, 43, 87, 121, 136, 180, 214, 229, 273)(29, 48, 81, 122,
141, 174, 215, 234, 267)(30, 53, 75, 123, 146, 168, 216, 239, 261)(31, 58, 69,
124, 151, 162, 217, 244, 255)
C4[ 279, 3 ]
279
-1 33 255 62 274
-2 275 34 256 32
-3 33 276 35 257
-4 34 277 36 258
-5 35 278 37 259
-6 36 279 38 260
-7 37 39 249 261
-8 38 40 250 262
-9 39 41 251 263
-10 264 40 42 252
-11 253 265 41 43
-12 44 254 266 42
-13 45 255 267 43
-14 44 46 256 268
-15 45 47 257 269
-16 46 48 258 270
-17 47 49 259 271
-18 48 50 260 272
-19 49 51 261 273
-20 50 52 262 274
-21 275 51 53 263
-22 264 276 52 54
-23 55 265 277 53
-24 56 266 278 54
-25 55 57 267 279
-26 56 58 268 249
-27 57 59 269 250
-28 58 60 270 251
-29 59 61 271 252
-30 253 60 62 272
-31 254 61 273 32
-32 89 2 68 31
-33 1 90 3 69
-34 2 91 4 70
-35 3 92 5 71
-36 4 93 6 72
-37 5 7 73 63
-38 6 8 74 64
-39 7 9 75 65
-40 66 8 10 76
-41 11 77 67 9
-42 12 78 68 10
-43 11 13 79 69
-44 12 14 80 70
-45 13 15 81 71
-46 14 16 82 72
-47 15 17 83 73
-48 16 18 84 74
-49 17 19 85 75
-50 18 20 86 76
-51 77 19 21 87
-52 22 88 78 20
-53 23 89 79 21
-54 22 24 90 80
-55 23 25 91 81
-56 24 26 92 82
-57 25 27 93 83
-58 26 28 84 63
-59 27 29 85 64
-60 28 30 86 65
-61 66 29 31 87
-62 88 1 67 30
-63 100 58 37 119
-64 101 59 38 120
-65 121 102 60 39
-66 122 103 61 40
-67 123 104 62 41
-68 124 105 42 32
-69 33 94 106 43
-70 44 34 95 107
-71 45 35 96 108
-72 46 36 97 109
-73 110 47 37 98
-74 99 111 48 38
-75 100 112 49 39
-76 101 113 50 40
-77 102 114 51 41
-78 103 115 52 42
-79 104 116 53 43
-80 44 105 117 54
-81 55 45 106 118
-82 56 46 107 119
-83 57 47 108 120
-84 121 58 48 109
-85 110 122 59 49
-86 111 123 60 50
-87 112 124 61 51
-88 113 94 62 52
-89 114 95 53 32
-90 33 115 96 54
-91 55 34 116 97
-92 56 35 117 98
-93 99 57 36 118
-94 88 155 69 126
-95 89 70 125 127
-96 90 71 126 128
-97 91 72 127 129
-98 92 73 128 130
-99 93 74 129 131
-100 132 63 75 130
-101 133 64 76 131
-102 77 132 134 65
-103 66 78 133 135
-104 67 79 134 136
-105 68 80 135 137
-106 69 81 136 138
-107 70 82 137 139
-108 71 83 138 140
-109 72 84 139 141
-110 73 85 140 142
-111 143 74 86 141
-112 144 75 87 142
-113 88 143 145 76
-114 77 89 144 146
-115 78 90 145 147
-116 79 91 146 148
-117 80 92 147 149
-118 81 93 148 150
-119 82 149 63 151
-120 83 150 64 152
-121 84 151 65 153
-122 66 154 85 152
-123 67 155 86 153
-124 154 68 125 87
-125 124 182 95 161
-126 94 183 96 162
-127 95 184 97 163
-128 96 185 98 164
-129 99 165 97 186
-130 100 166 156 98
-131 99 101 167 157
-132 100 102 168 158
-133 101 103 169 159
-134 102 104 170 160
-135 103 105 171 161
-136 104 106 172 162
-137 105 107 173 163
-138 106 108 174 164
-139 165 107 109 175
-140 110 176 166 108
-141 111 177 167 109
-142 110 112 178 168
-143 111 113 179 169
-144 112 114 180 170
-145 113 115 181 171
-146 114 116 182 172
-147 115 117 183 173
-148 116 118 184 174
-149 117 119 185 175
-150 176 118 120 186
-151 121 177 156 119
-152 122 178 157 120
-153 121 123 179 158
-154 122 124 180 159
-155 123 181 94 160
-156 212 193 151 130
-157 213 194 152 131
-158 132 214 195 153
-159 154 133 215 196
-160 155 134 216 197
-161 198 135 125 217
-162 187 199 136 126
-163 188 200 137 127
-164 189 201 138 128
-165 190 202 139 129
-166 191 203 140 130
-167 192 204 141 131
-168 132 193 205 142
-169 143 133 194 206
-170 144 134 195 207
-171 145 135 196 208
-172 209 146 136 197
-173 198 210 147 137
-174 199 211 148 138
-175 200 212 149 139
-176 201 213 150 140
-177 202 214 151 141
-178 203 215 152 142
-179 143 204 216 153
-180 154 144 205 217
-181 187 155 145 206
-182 188 146 125 207
-183 189 147 126 208
-184 209 190 148 127
-185 210 191 149 128
-186 211 192 150 129
-187 181 248 162 219
-188 220 182 163 218
-189 221 183 164 219
-190 165 220 222 184
-191 166 221 223 185
-192 167 222 224 186
-193 156 168 223 225
-194 157 169 224 226
-195 158 170 225 227
-196 159 171 226 228
-197 160 172 227 229
-198 161 173 228 230
-199 231 162 174 229
-200 232 163 175 230
-201 176 231 233 164
-202 165 177 232 234
-203 166 178 233 235
-204 167 179 234 236
-205 168 180 235 237
-206 169 181 236 238
-207 170 182 237 239
-208 171 183 238 240
-209 172 184 239 241
-210 242 173 185 240
-211 243 174 186 241
-212 242 156 244 175
-213 176 243 157 245
-214 177 244 158 246
-215 178 245 159 247
-216 179 246 160 248
-217 180 247 161 218
-218 275 188 254 217
-219 187 276 189 255
-220 188 277 190 256
-221 189 278 191 257
-222 190 279 192 258
-223 191 193 259 249
-224 192 194 260 250
-225 193 195 261 251
-226 194 196 262 252
-227 253 195 197 263
-228 198 264 254 196
-229 199 265 255 197
-230 198 200 266 256
-231 199 201 267 257
-232 200 202 268 258
-233 201 203 269 259
-234 202 204 270 260
-235 203 205 271 261
-236 204 206 272 262
-237 205 207 273 263
-238 264 206 208 274
-239 209 275 265 207
-240 210 276 266 208
-241 209 211 277 267
-242 210 212 278 268
-243 211 213 279 269
-244 212 214 270 249
-245 213 215 271 250
-246 214 216 272 251
-247 215 217 273 252
-248 187 253 216 274
-249 244 223 26 7
-250 245 224 27 8
-251 246 225 28 9
-252 247 226 29 10
-253 11 248 227 30
-254 12 228 31 218
-255 1 13 229 219
-256 220 2 14 230
-257 231 221 3 15
-258 232 222 4 16
-259 233 223 5 17
-260 234 224 6 18
-261 235 225 7 19
-262 236 226 8 20
-263 237 227 9 21
-264 22 238 228 10
-265 11 23 239 229
-266 12 24 240 230
-267 231 13 25 241
-268 242 232 14 26
-269 243 233 15 27
-270 244 234 16 28
-271 245 235 17 29
-272 246 236 18 30
-273 247 237 19 31
-274 1 248 238 20
-275 2 239 218 21
-276 22 3 240 219
-277 220 23 4 241
-278 242 221 24 5
-279 243 222 25 6
0