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