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