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