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