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