Graph forms
for C4 [ 285, 4 ] = PS(15,19;7)
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On this page are computer-accessible forms for the graph C4[ 285, 4 ] =
PS(15,19;7).
(I) Following is a form readable by MAGMA:
g:=Graph<285|{ {76, 77}, {190, 191}, {133, 134}, {19, 20}, {264, 271}, {32, 39},
{152, 159}, {208, 215}, {50, 58}, {114, 122}, {113, 121}, {112, 120}, {51, 59},
{52, 60}, {53, 61}, {54, 62}, {55, 63}, {164, 172}, {165, 173}, {166, 174},
{167, 175}, {224, 232}, {225, 233}, {226, 234}, {227, 235}, {228, 236}, {33,
40}, {263, 270}, {261, 268}, {35, 42}, {37, 44}, {147, 154}, {149, 156}, {151,
158}, {209, 216}, {34, 41}, {262, 269}, {112, 123}, {38, 45}, {48, 59}, {52,
63}, {146, 153}, {150, 157}, {164, 175}, {224, 235}, {228, 239}, {32, 44}, {259,
271}, {258, 270}, {257, 269}, {256, 268}, {33, 45}, {34, 46}, {35, 47}, {144,
156}, {145, 157}, {146, 158}, {147, 159}, {208, 220}, {209, 221}, {49, 60},
{113, 124}, {51, 62}, {161, 172}, {163, 174}, {225, 236}, {227, 238}, {36, 43},
{260, 267}, {247, 248}, {114, 125}, {50, 61}, {148, 155}, {162, 173}, {226,
237}, {4, 22}, {237, 255}, {236, 254}, {233, 251}, {133, 151}, {132, 150}, {129,
147}, {128, 146}, {76, 94}, {5, 23}, {8, 26}, {9, 27}, {12, 30}, {13, 31}, {64,
82}, {65, 83}, {68, 86}, {69, 87}, {72, 90}, {73, 91}, {173, 191}, {232, 250},
{1, 21}, {263, 275}, {262, 274}, {261, 273}, {260, 272}, {235, 255}, {234, 254},
{233, 253}, {131, 151}, {130, 150}, {129, 149}, {128, 148}, {75, 95}, {2, 22},
{3, 23}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {36, 48}, {37, 49}, {38, 50},
{64, 84}, {65, 85}, {66, 86}, {67, 87}, {72, 92}, {73, 93}, {74, 94}, {141,
153}, {142, 154}, {143, 155}, {198, 210}, {199, 211}, {204, 216}, {205, 217},
{206, 218}, {207, 219}, {232, 252}, {47, 58}, {111, 122}, {109, 120}, {165,
176}, {167, 178}, {2, 20}, {235, 253}, {234, 252}, {131, 149}, {130, 148}, {75,
93}, {3, 21}, {10, 28}, {11, 29}, {66, 84}, {67, 85}, {74, 92}, {110, 121},
{166, 177}, {107, 115}, {111, 119}, {110, 118}, {109, 117}, {108, 116}, {168,
176}, {169, 177}, {170, 178}, {171, 179}, {203, 210}, {265, 272}, {205, 212},
{207, 214}, {192, 218}, {257, 283}, {256, 282}, {193, 219}, {196, 222}, {197,
223}, {96, 123}, {266, 273}, {108, 119}, {104, 115}, {100, 127}, {160, 187},
{168, 179}, {206, 213}, {4, 24}, {266, 278}, {265, 277}, {264, 276}, {132, 152},
{5, 25}, {6, 26}, {7, 27}, {68, 88}, {69, 89}, {70, 90}, {71, 91}, {200, 212},
{201, 213}, {202, 214}, {203, 215}, {229, 249}, {230, 250}, {231, 251}, {97,
124}, {107, 118}, {105, 116}, {99, 126}, {161, 188}, {163, 190}, {169, 180},
{171, 182}, {6, 24}, {259, 285}, {258, 284}, {97, 127}, {96, 126}, {7, 25}, {70,
88}, {71, 89}, {160, 190}, {194, 220}, {195, 221}, {230, 248}, {231, 249}, {98,
125}, {106, 117}, {162, 189}, {170, 181}, {192, 223}, {204, 211}, {21, 52},
{135, 166}, {83, 114}, {81, 112}, {79, 110}, {77, 108}, {23, 54}, {25, 56},
{137, 168}, {139, 170}, {193, 224}, {195, 226}, {197, 228}, {154, 184}, {155,
185}, {158, 188}, {159, 189}, {210, 240}, {211, 241}, {214, 244}, {215, 245},
{22, 53}, {134, 165}, {82, 113}, {78, 109}, {26, 57}, {138, 169}, {194, 225},
{157, 184}, {159, 186}, {213, 240}, {215, 242}, {22, 48}, {135, 161}, {134,
160}, {87, 113}, {86, 112}, {79, 105}, {78, 104}, {23, 49}, {30, 56}, {31, 57},
{142, 168}, {143, 169}, {156, 186}, {157, 187}, {198, 224}, {199, 225}, {212,
242}, {213, 243}, {1, 38}, {20, 51}, {140, 171}, {158, 185}, {196, 227}, {214,
241}, {24, 50}, {137, 163}, {136, 162}, {88, 114}, {77, 103}, {25, 51}, {28,
54}, {29, 55}, {140, 166}, {141, 167}, {200, 226}, {201, 227}, {156, 183}, {216,
243}, {220, 247}, {12, 32}, {13, 33}, {14, 34}, {15, 35}, {153, 180}, {155,
182}, {217, 244}, {219, 246}, {14, 32}, {15, 33}, {26, 52}, {27, 53}, {138,
164}, {139, 165}, {153, 183}, {202, 228}, {216, 246}, {217, 247}, {24, 55},
{136, 167}, {154, 181}, {218, 245}, {16, 34}, {17, 35}, {16, 36}, {95, 107},
{94, 106}, {93, 105}, {92, 104}, {87, 99}, {86, 98}, {85, 97}, {84, 96}, {17,
37}, {18, 38}, {28, 40}, {29, 41}, {30, 42}, {31, 43}, {148, 160}, {149, 161},
{150, 162}, {151, 163}, {221, 232}, {223, 234}, {18, 36}, {19, 37}, {222, 233},
{221, 229}, {222, 230}, {223, 231}, {89, 96}, {95, 102}, {93, 100}, {91, 98},
{20, 46}, {85, 111}, {84, 110}, {81, 107}, {80, 106}, {21, 47}, {144, 170},
{145, 171}, {90, 97}, {94, 101}, {212, 239}, {220, 231}, {27, 39}, {91, 103},
{90, 102}, {89, 101}, {88, 100}, {152, 164}, {211, 238}, {219, 230}, {82, 108},
{83, 109}, {80, 111}, {92, 99}, {210, 237}, {218, 229}, {191, 222}, {39, 69},
{42, 72}, {43, 73}, {46, 76}, {39, 66}, {45, 72}, {47, 74}, {58, 95}, {44, 74},
{45, 75}, {191, 217}, {46, 73}, {40, 67}, {44, 71}, {60, 80}, {61, 81}, {62,
82}, {63, 83}, {172, 192}, {173, 193}, {174, 194}, {175, 195}, {188, 208}, {189,
209}, {41, 68}, {43, 70}, {40, 70}, {41, 71}, {62, 80}, {63, 81}, {174, 192},
{175, 193}, {190, 208}, {42, 69}, {60, 78}, {61, 79}, {176, 194}, {177, 195},
{180, 198}, {181, 199}, {184, 202}, {185, 203}, {188, 206}, {189, 207}, {58,
78}, {59, 79}, {176, 196}, {177, 197}, {178, 198}, {179, 199}, {184, 204}, {185,
205}, {186, 206}, {187, 207}, {53, 64}, {55, 66}, {59, 77}, {178, 196}, {179,
197}, {186, 204}, {187, 205}, {54, 65}, {56, 64}, {57, 65}, {48, 75}, {56, 67},
{180, 200}, {181, 201}, {182, 202}, {183, 203}, {49, 76}, {57, 68}, {172, 209},
{182, 200}, {183, 201}, {98, 128}, {103, 133}, {102, 132}, {99, 129}, {101,
128}, {103, 130}, {100, 130}, {101, 131}, {102, 129}, {104, 131}, {115, 152},
{124, 144}, {127, 147}, {126, 146}, {125, 145}, {105, 132}, {126, 144}, {127,
145}, {106, 133}, {116, 134}, {125, 143}, {124, 142}, {121, 139}, {120, 138},
{117, 135}, {115, 135}, {123, 143}, {122, 142}, {121, 141}, {120, 140}, {122,
140}, {123, 141}, {116, 136}, {119, 139}, {118, 138}, {117, 137}, {118, 136},
{119, 137}, {13, 268}, {15, 270}, {17, 272}, {19, 274}, {9, 267}, {12, 270},
{13, 271}, {16, 274}, {17, 275}, {14, 269}, {18, 273}, {10, 268}, {11, 269},
{18, 276}, {19, 277}, {12, 267}, {1, 275}, {4, 278}, {5, 279}, {8, 282}, {9,
283}, {2, 279}, {8, 285}, {2, 276}, {3, 277}, {10, 284}, {11, 285}, {1, 278},
{3, 280}, {7, 284}, {4, 281}, {6, 283}, {6, 280}, {7, 281}, {14, 272}, {15,
273}, {5, 282}, {16, 271}, {249, 280}, {253, 284}, {251, 282}, {250, 281}, {254,
285}, {254, 280}, {255, 281}, {252, 283}, {248, 274}, {253, 279}, {252, 278},
{249, 275}, {236, 256}, {239, 259}, {238, 258}, {237, 257}, {238, 256}, {251,
277}, {250, 276}, {239, 257}, {229, 266}, {248, 279}, {240, 258}, {245, 263},
{244, 262}, {241, 259}, {240, 260}, {255, 267}, {243, 263}, {242, 262}, {241,
261}, {242, 260}, {243, 261}, {244, 264}, {246, 266}, {245, 265}, {246, 264},
{247, 265} }>;
(II) A more general form is to represent the graph as the orbit of {76, 77}
under the group generated by the following permutations:
a: (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, 280, 281, 282, 283, 284, 285) (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, 19)(3, 18)(4, 17)(5, 16)(6, 15)(7, 14)(8, 13)(9, 12)(10, 11)(21, 38)(22,
37)(23, 36)(24, 35)(25, 34)(26, 33)(27, 32)(28, 31)(29, 30)(40, 57)(41, 56)(42,
55)(43, 54)(44, 53)(45, 52)(46, 51)(47, 50)(48, 49)(59, 76)(60, 75)(61, 74)(62,
73)(63, 72)(64, 71)(65, 70)(66, 69)(67, 68)(78, 95)(79, 94)(80, 93)(81, 92)(82,
91)(83, 90)(84, 89)(85, 88)(86, 87)(97, 114)(98, 113)(99, 112)(100, 111)(101,
110)(102, 109)(103, 108)(104, 107)(105, 106)(116, 133)(117, 132)(118, 131)(119,
130)(120, 129)(121, 128)(122, 127)(123, 126)(124, 125)(135, 152)(136, 151)(137,
150)(138, 149)(139, 148)(140, 147)(141, 146)(142, 145)(143, 144)(154, 171)(155,
170)(156, 169)(157, 168)(158, 167)(159, 166)(160, 165)(161, 164)(162, 163)(173,
190)(174, 189)(175, 188)(176, 187)(177, 186)(178, 185)(179, 184)(180, 183)(181,
182)(192, 209)(193, 208)(194, 207)(195, 206)(196, 205)(197, 204)(198, 203)(199,
202)(200, 201)(211, 228)(212, 227)(213, 226)(214, 225)(215, 224)(216, 223)(217,
222)(218, 221)(219, 220)(230, 247)(231, 246)(232, 245)(233, 244)(234, 243)(235,
242)(236, 241)(237, 240)(238, 239)(249, 266)(250, 265)(251, 264)(252, 263)(253,
262)(254, 261)(255, 260)(256, 259)(257, 258)(268, 285)(269, 284)(270, 283)(271,
282)(272, 281)(273, 280)(274, 279)(275, 278)(276, 277)
c: (1, 20, 39, 58, 77, 96, 115, 134, 153, 172, 191, 210, 229, 248, 267)(2, 32,
50, 76, 84, 104, 116, 146, 164, 190, 198, 218, 230, 260, 278, 19, 27, 47, 59,
89, 107, 133, 141, 161, 173, 203, 221, 247, 255, 275)(3, 25, 42, 75, 91, 112,
117, 139, 156, 189, 205, 226, 231, 253, 270, 18, 34, 55, 60, 82, 99, 132, 148,
169, 174, 196, 213, 246, 262, 283)(4, 37, 53, 74, 79, 101, 118, 151, 167, 188,
193, 215, 232, 265, 281, 17, 22, 44, 61, 94, 110, 131, 136, 158, 175, 208, 224,
245, 250, 272)(5, 30, 45, 73, 86, 109, 119, 144, 159, 187, 200, 223, 233, 258,
273, 16, 29, 52, 62, 87, 102, 130, 143, 166, 176, 201, 216, 244, 257, 280)(6,
23, 56, 72, 93, 98, 120, 137, 170, 186, 207, 212, 234, 251, 284, 15, 36, 41, 63,
80, 113, 129, 150, 155, 177, 194, 227, 243, 264, 269)(7, 35, 48, 71, 81, 106,
121, 149, 162, 185, 195, 220, 235, 263, 276, 14, 24, 49, 64, 92, 105, 128, 138,
163, 178, 206, 219, 242, 252, 277)(8, 28, 40, 70, 88, 114, 122, 142, 154, 184,
202, 228, 236, 256, 268, 13, 31, 57, 65, 85, 97, 127, 145, 171, 179, 199, 211,
241, 259, 285)(9, 21, 51, 69, 95, 103, 123, 135, 165, 183, 209, 217, 237, 249,
279, 12, 38, 46, 66, 78, 108, 126, 152, 160, 180, 192, 222, 240, 266, 274)(10,
33, 43, 68, 83, 111, 124, 147, 157, 182, 197, 225, 238, 261, 271, 11, 26, 54,
67, 90, 100, 125, 140, 168, 181, 204, 214, 239, 254, 282)
C4[ 285, 4 ]
285
-1 275 278 38 21
-2 22 276 279 20
-3 23 277 280 21
-4 22 24 278 281
-5 23 25 279 282
-6 24 26 280 283
-7 25 27 281 284
-8 26 28 282 285
-9 267 27 29 283
-10 268 28 30 284
-11 269 29 31 285
-12 267 270 30 32
-13 33 268 271 31
-14 34 269 272 32
-15 33 35 270 273
-16 34 36 271 274
-17 275 35 37 272
-18 276 36 38 273
-19 277 37 20 274
-20 2 46 51 19
-21 1 3 47 52
-22 2 4 48 53
-23 3 5 49 54
-24 55 4 6 50
-25 56 5 7 51
-26 57 6 8 52
-27 39 7 9 53
-28 40 8 10 54
-29 11 55 41 9
-30 12 56 42 10
-31 11 13 57 43
-32 44 12 14 39
-33 45 13 15 40
-34 46 14 16 41
-35 47 15 17 42
-36 48 16 18 43
-37 44 49 17 19
-38 1 45 50 18
-39 66 69 27 32
-40 33 67 70 28
-41 34 68 71 29
-42 35 69 72 30
-43 36 70 73 31
-44 37 71 74 32
-45 33 38 72 75
-46 34 73 20 76
-47 35 58 74 21
-48 22 36 59 75
-49 23 37 60 76
-50 24 58 38 61
-51 25 59 62 20
-52 26 60 63 21
-53 22 27 61 64
-54 23 28 62 65
-55 66 24 29 63
-56 67 25 30 64
-57 68 26 31 65
-58 78 47 50 95
-59 77 79 48 51
-60 78 80 49 52
-61 79 81 50 53
-62 80 82 51 54
-63 55 81 83 52
-64 56 82 84 53
-65 57 83 85 54
-66 55 39 84 86
-67 56 40 85 87
-68 88 57 41 86
-69 89 39 42 87
-70 88 90 40 43
-71 44 89 91 41
-72 45 90 92 42
-73 46 91 93 43
-74 44 47 92 94
-75 45 48 93 95
-76 77 46 49 94
-77 59 103 108 76
-78 58 60 104 109
-79 110 59 61 105
-80 111 60 62 106
-81 112 61 63 107
-82 113 62 64 108
-83 114 63 65 109
-84 66 110 96 64
-85 67 111 97 65
-86 66 68 112 98
-87 99 67 69 113
-88 100 68 70 114
-89 101 69 71 96
-90 102 70 72 97
-91 103 71 73 98
-92 99 104 72 74
-93 100 105 73 75
-94 101 106 74 76
-95 58 102 107 75
-96 89 123 126 84
-97 90 124 127 85
-98 91 125 128 86
-99 92 126 129 87
-100 88 93 127 130
-101 89 94 128 131
-102 132 90 95 129
-103 77 133 91 130
-104 78 92 115 131
-105 132 79 93 116
-106 133 80 94 117
-107 81 115 95 118
-108 77 82 116 119
-109 78 83 117 120
-110 121 79 84 118
-111 122 80 85 119
-112 123 81 86 120
-113 121 124 82 87
-114 88 122 125 83
-115 135 104 107 152
-116 134 136 105 108
-117 135 137 106 109
-118 110 136 138 107
-119 111 137 139 108
-120 112 138 140 109
-121 110 113 139 141
-122 111 114 140 142
-123 143 112 96 141
-124 144 113 97 142
-125 143 145 114 98
-126 99 144 146 96
-127 100 145 147 97
-128 101 146 148 98
-129 99 102 147 149
-130 100 103 148 150
-131 101 104 149 151
-132 102 105 150 152
-133 134 103 106 151
-134 165 133 116 160
-135 166 115 117 161
-136 167 116 118 162
-137 168 117 119 163
-138 169 118 120 164
-139 121 165 170 119
-140 122 166 171 120
-141 121 123 167 153
-142 154 122 124 168
-143 155 123 125 169
-144 156 124 126 170
-145 157 125 127 171
-146 158 126 128 153
-147 154 159 127 129
-148 155 160 128 130
-149 156 161 129 131
-150 132 157 162 130
-151 133 158 163 131
-152 132 115 159 164
-153 146 180 183 141
-154 147 181 184 142
-155 143 148 182 185
-156 144 149 183 186
-157 187 145 150 184
-158 188 146 151 185
-159 189 147 152 186
-160 187 134 190 148
-161 188 135 149 172
-162 189 136 150 173
-163 190 137 151 174
-164 138 172 152 175
-165 176 134 139 173
-166 177 135 140 174
-167 178 136 141 175
-168 176 179 137 142
-169 143 177 180 138
-170 144 178 181 139
-171 145 179 182 140
-172 209 192 161 164
-173 165 191 193 162
-174 166 192 194 163
-175 167 193 195 164
-176 165 168 194 196
-177 166 169 195 197
-178 198 167 170 196
-179 199 168 171 197
-180 198 200 169 153
-181 154 199 201 170
-182 155 200 202 171
-183 156 201 203 153
-184 154 157 202 204
-185 155 158 203 205
-186 156 159 204 206
-187 157 160 205 207
-188 158 161 206 208
-189 209 159 162 207
-190 191 160 163 208
-191 222 190 173 217
-192 223 172 174 218
-193 224 173 175 219
-194 176 220 225 174
-195 177 221 226 175
-196 176 178 222 227
-197 177 179 223 228
-198 210 178 180 224
-199 211 179 181 225
-200 212 180 182 226
-201 213 181 183 227
-202 214 182 184 228
-203 210 215 183 185
-204 211 216 184 186
-205 187 212 217 185
-206 188 213 218 186
-207 187 189 214 219
-208 220 188 190 215
-209 221 189 172 216
-210 198 203 237 240
-211 199 204 238 241
-212 242 200 205 239
-213 243 201 206 240
-214 244 202 207 241
-215 242 245 203 208
-216 209 243 246 204
-217 244 191 247 205
-218 245 192 206 229
-219 246 193 207 230
-220 231 247 194 208
-221 209 232 195 229
-222 233 191 196 230
-223 231 234 192 197
-224 198 232 235 193
-225 199 233 236 194
-226 200 234 237 195
-227 201 235 238 196
-228 202 236 239 197
-229 221 266 249 218
-230 222 248 250 219
-231 220 223 249 251
-232 221 224 250 252
-233 253 222 225 251
-234 254 223 226 252
-235 253 255 224 227
-236 254 256 225 228
-237 210 255 257 226
-238 211 256 258 227
-239 212 257 259 228
-240 210 213 258 260
-241 211 214 259 261
-242 212 215 260 262
-243 213 216 261 263
-244 264 214 217 262
-245 265 215 218 263
-246 264 266 216 219
-247 220 265 248 217
-248 279 247 230 274
-249 231 275 280 229
-250 232 276 281 230
-251 231 233 277 282
-252 232 234 278 283
-253 233 235 279 284
-254 234 236 280 285
-255 267 235 237 281
-256 268 236 238 282
-257 269 237 239 283
-258 270 238 240 284
-259 271 239 241 285
-260 242 267 272 240
-261 243 268 273 241
-262 242 244 269 274
-263 275 243 245 270
-264 276 244 246 271
-265 277 245 247 272
-266 278 246 229 273
-267 12 255 260 9
-268 13 256 261 10
-269 11 14 257 262
-270 12 15 258 263
-271 264 13 16 259
-272 265 14 17 260
-273 266 15 18 261
-274 16 248 19 262
-275 1 17 249 263
-276 264 2 18 250
-277 265 3 19 251
-278 1 266 4 252
-279 253 2 5 248
-280 254 3 6 249
-281 255 4 7 250
-282 256 5 8 251
-283 257 6 9 252
-284 253 258 7 10
-285 11 254 259 8
0