Graph forms
for C4 [ 216, 29 ] = AMC(24,3,[0.1:1.2])
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On this page are computer-accessible forms for the graph C4[ 216, 29 ] =
AMC(24,3,[0.1:1.2]).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {36, 37}, {108, 109}, {72, 73}, {144, 145}, {180, 181}, {8, 11},
{188, 191}, {80, 83}, {44, 47}, {116, 119}, {152, 155}, {24, 28}, {107, 111},
{106, 110}, {99, 103}, {96, 100}, {27, 31}, {34, 38}, {35, 39}, {168, 172},
{171, 175}, {178, 182}, {179, 183}, {9, 12}, {187, 190}, {104, 109}, {81, 84},
{72, 77}, {32, 37}, {43, 46}, {115, 118}, {144, 149}, {153, 156}, {176, 181},
{8, 14}, {185, 191}, {184, 190}, {99, 101}, {98, 100}, {81, 87}, {80, 86}, {9,
15}, {26, 28}, {27, 29}, {40, 46}, {41, 47}, {112, 118}, {113, 119}, {152, 158},
{153, 159}, {170, 172}, {171, 173}, {25, 30}, {192, 199}, {105, 110}, {97, 102},
{33, 38}, {48, 55}, {120, 127}, {169, 174}, {177, 182}, {17, 25}, {198, 206},
{197, 205}, {195, 203}, {194, 202}, {192, 200}, {103, 111}, {87, 95}, {86, 94},
{84, 92}, {83, 91}, {70, 78}, {18, 26}, {34, 42}, {48, 56}, {50, 58}, {51, 59},
{53, 61}, {54, 62}, {67, 75}, {119, 127}, {161, 169}, {162, 170}, {178, 186},
{23, 30}, {195, 202}, {97, 104}, {87, 94}, {51, 58}, {131, 138}, {133, 140},
{167, 174}, {6, 12}, {197, 207}, {196, 206}, {193, 203}, {85, 95}, {69, 79}, {7,
13}, {16, 26}, {17, 27}, {33, 43}, {49, 59}, {52, 62}, {53, 63}, {114, 120},
{115, 121}, {150, 156}, {151, 157}, {160, 170}, {161, 171}, {177, 187}, {16,
27}, {198, 205}, {196, 207}, {98, 105}, {96, 107}, {71, 76}, {18, 25}, {20, 31},
{22, 29}, {35, 40}, {52, 63}, {54, 61}, {128, 139}, {130, 137}, {132, 143},
{134, 141}, {160, 171}, {162, 169}, {164, 175}, {166, 173}, {179, 184}, {1, 13},
{71, 75}, {70, 74}, {2, 14}, {3, 15}, {112, 124}, {113, 125}, {114, 126}, {132,
136}, {135, 139}, {145, 157}, {146, 158}, {147, 159}, {7, 10}, {193, 204}, {32,
45}, {36, 41}, {49, 60}, {64, 77}, {68, 73}, {117, 120}, {129, 140}, {131, 142},
{151, 154}, {176, 189}, {180, 185}, {4, 10}, {194, 204}, {83, 93}, {82, 92}, {5,
11}, {50, 60}, {65, 79}, {66, 76}, {116, 122}, {117, 123}, {134, 136}, {135,
137}, {148, 154}, {149, 155}, {65, 78}, {84, 91}, {82, 93}, {69, 74}, {129,
142}, {133, 138}, {128, 144}, {200, 216}, {199, 215}, {163, 179}, {164, 180},
{1, 16}, {100, 117}, {75, 90}, {73, 88}, {3, 18}, {37, 52}, {39, 54}, {64, 81},
{109, 124}, {111, 126}, {136, 153}, {172, 189}, {66, 80}, {202, 216}, {199,
213}, {102, 116}, {130, 144}, {138, 152}, {163, 177}, {166, 180}, {174, 188},
{2, 17}, {103, 116}, {74, 89}, {38, 53}, {67, 80}, {110, 125}, {139, 152}, {175,
188}, {4, 16}, {78, 90}, {77, 89}, {76, 88}, {5, 17}, {6, 18}, {37, 49}, {38,
50}, {39, 51}, {109, 121}, {110, 122}, {111, 123}, {13, 24}, {100, 113}, {68,
81}, {140, 153}, {165, 176}, {167, 178}, {172, 185}, {14, 24}, {102, 112}, {101,
115}, {46, 56}, {47, 57}, {173, 187}, {174, 184}, {46, 57}, {101, 114}, {165,
178}, {173, 186}, {11, 19}, {106, 114}, {12, 20}, {14, 22}, {15, 23}, {47, 55},
{139, 147}, {142, 150}, {175, 183}, {15, 22}, {205, 212}, {203, 210}, {169,
176}, {13, 23}, {105, 115}, {79, 85}, {78, 84}, {42, 48}, {43, 49}, {141, 151},
{107, 112}, {206, 213}, {204, 215}, {202, 209}, {200, 211}, {143, 148}, {168,
179}, {170, 177}, {40, 52}, {207, 211}, {204, 208}, {75, 87}, {74, 86}, {73,
85}, {41, 53}, {42, 54}, {142, 146}, {143, 147}, {45, 48}, {203, 214}, {201,
212}, {108, 113}, {104, 117}, {79, 82}, {136, 149}, {140, 145}, {10, 20}, {207,
209}, {206, 208}, {77, 83}, {76, 82}, {11, 21}, {44, 50}, {45, 51}, {137, 151},
{138, 148}, {10, 21}, {205, 210}, {201, 214}, {12, 19}, {137, 150}, {141, 146},
{19, 35}, {92, 108}, {91, 107}, {20, 36}, {28, 45}, {145, 160}, {147, 162}, {19,
33}, {94, 108}, {91, 105}, {22, 36}, {30, 44}, {31, 44}, {146, 161}, {148, 160},
{149, 161}, {150, 162}, {21, 32}, {95, 106}, {93, 104}, {85, 96}, {23, 34}, {28,
41}, {157, 168}, {29, 43}, {86, 96}, {30, 40}, {158, 168}, {21, 34}, {93, 106},
{29, 42}, {31, 39}, {90, 98}, {89, 97}, {155, 163}, {156, 164}, {158, 166},
{159, 167}, {25, 32}, {95, 102}, {159, 166}, {88, 98}, {89, 99}, {157, 167},
{24, 35}, {94, 101}, {92, 103}, {90, 97}, {88, 99}, {26, 33}, {154, 164}, {155,
165}, {154, 165}, {156, 163}, {55, 71}, {56, 72}, {181, 196}, {183, 198}, {55,
69}, {58, 72}, {182, 197}, {181, 193}, {182, 194}, {183, 195}, {190, 200}, {191,
201}, {190, 201}, {191, 199}, {59, 66}, {61, 68}, {186, 192}, {187, 193}, {56,
67}, {58, 65}, {60, 71}, {62, 69}, {60, 64}, {186, 198}, {185, 197}, {184, 196},
{63, 67}, {57, 68}, {189, 192}, {59, 70}, {62, 64}, {189, 195}, {188, 194}, {63,
65}, {57, 70}, {61, 66}, {3, 211}, {6, 214}, {7, 213}, {4, 215}, {2, 214}, {3,
215}, {1, 212}, {5, 208}, {4, 210}, {7, 209}, {2, 213}, {6, 209}, {1, 216}, {9,
208}, {8, 210}, {8, 211}, {5, 216}, {9, 212}, {127, 143}, {127, 141}, {118,
128}, {119, 129}, {118, 129}, {120, 128}, {122, 130}, {123, 131}, {125, 133},
{126, 134}, {123, 130}, {121, 131}, {124, 134}, {125, 135}, {124, 135}, {126,
133}, {121, 132}, {122, 132} }>;
(II) A more general form is to represent the graph as the orbit of {36, 37}
under the group generated by the following permutations:
a: (1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145,
154, 163, 172, 181, 190, 199, 208)(2, 15, 27, 34, 39, 53, 59, 67, 74, 87, 99,
106, 111, 125, 131, 139, 146, 159, 171, 178, 183, 197, 203, 211)(3, 17, 23, 31,
38, 51, 63, 70, 75, 89, 95, 103, 110, 123, 135, 142, 147, 161, 167, 175, 182,
195, 207, 214)(4, 11, 24, 36, 43, 48, 62, 68, 76, 83, 96, 108, 115, 120, 134,
140, 148, 155, 168, 180, 187, 192, 206, 212)(5, 13, 20, 33, 45, 52, 57, 71, 77,
85, 92, 105, 117, 124, 129, 143, 149, 157, 164, 177, 189, 196, 201, 215)(6, 18,
25, 30, 44, 50, 58, 65, 78, 90, 97, 102, 116, 122, 130, 137, 150, 162, 169, 174,
188, 194, 202, 209)(7, 12, 26, 32, 40, 47, 60, 72, 79, 84, 98, 104, 112, 119,
132, 144, 151, 156, 170, 176, 184, 191, 204, 216)(8, 14, 22, 29, 42, 54, 61, 66,
80, 86, 94, 101, 114, 126, 133, 138, 152, 158, 166, 173, 186, 198, 205, 210)(9,
16, 21, 35, 41, 49, 56, 69, 81, 88, 93, 107, 113, 121, 128, 141, 153, 160, 165,
179, 185, 193, 200, 213) (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, 6, 3, 8)(4, 5, 7, 9)(10, 208)(11, 213, 12, 215)(13, 212, 16, 216)(14,
214, 18, 211)(15, 210, 17, 209)(19, 199)(20, 204, 21, 206)(22, 203, 25, 207)(23,
205, 27, 202)(24, 201, 26, 200)(28, 190)(29, 195, 30, 197)(31, 194, 34, 198)(32,
196, 36, 193)(33, 192, 35, 191)(37, 181)(38, 186, 39, 188)(40, 185, 43, 189)(41,
187, 45, 184)(42, 183, 44, 182)(46, 172)(47, 177, 48, 179)(49, 176, 52, 180)(50,
178, 54, 175)(51, 174, 53, 173)(55, 163)(56, 168, 57, 170)(58, 167, 61, 171)(59,
169, 63, 166)(60, 165, 62, 164)(64, 154)(65, 159, 66, 161)(67, 158, 70, 162)(68,
160, 72, 157)(69, 156, 71, 155)(73, 145)(74, 150, 75, 152)(76, 149, 79, 153)(77,
151, 81, 148)(78, 147, 80, 146)(82, 136)(83, 141, 84, 143)(85, 140, 88, 144)(86,
142, 90, 139)(87, 138, 89, 137)(91, 127)(92, 132, 93, 134)(94, 131, 97, 135)(95,
133, 99, 130)(96, 129, 98, 128)(100, 118)(101, 123, 102, 125)(103, 122, 106,
126)(104, 124, 108, 121)(105, 120, 107, 119)(110, 114, 111, 116)(112, 113, 115,
117)
c: (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)
C4[ 216, 29 ]
216
-1 13 212 16 216
-2 14 213 214 17
-3 211 15 215 18
-4 210 16 215 10
-5 11 17 216 208
-6 209 12 214 18
-7 209 13 213 10
-8 11 210 211 14
-9 12 212 15 208
-10 4 7 20 21
-11 5 8 19 21
-12 6 19 9 20
-13 1 23 24 7
-14 22 2 24 8
-15 22 23 3 9
-16 1 4 26 27
-17 2 25 5 27
-18 3 25 26 6
-19 11 33 12 35
-20 12 36 31 10
-21 11 34 10 32
-22 14 36 15 29
-23 34 13 15 30
-24 13 35 14 28
-25 17 18 30 32
-26 33 16 28 18
-27 16 17 29 31
-28 45 24 26 41
-29 22 27 42 43
-30 44 23 25 40
-31 44 27 39 20
-32 45 25 37 21
-33 26 38 19 43
-34 23 38 42 21
-35 24 39 40 19
-36 22 37 41 20
-37 36 49 52 32
-38 33 34 50 53
-39 35 51 31 54
-40 35 46 30 52
-41 36 47 28 53
-42 34 48 29 54
-43 33 46 49 29
-44 47 50 30 31
-45 48 28 51 32
-46 56 57 40 43
-47 44 55 57 41
-48 55 45 56 42
-49 37 59 60 43
-50 44 58 38 60
-51 45 58 59 39
-52 37 40 62 63
-53 38 61 41 63
-54 39 61 62 42
-55 47 69 48 71
-56 67 46 48 72
-57 46 68 47 70
-58 50 72 51 65
-59 66 70 49 51
-60 49 71 50 64
-61 66 68 53 54
-62 69 52 64 54
-63 67 52 53 65
-64 77 81 60 62
-65 78 79 58 63
-66 80 59 61 76
-67 56 80 63 75
-68 57 81 61 73
-69 55 79 62 74
-70 78 57 59 74
-71 55 60 75 76
-72 77 56 58 73
-73 88 68 72 85
-74 89 69 70 86
-75 67 90 71 87
-76 66 88 71 82
-77 89 72 83 64
-78 90 70 84 65
-79 69 82 85 65
-80 66 67 83 86
-81 68 84 64 87
-82 79 92 93 76
-83 77 80 91 93
-84 78 91 81 92
-85 79 73 95 96
-86 80 94 74 96
-87 81 94 95 75
-88 99 73 76 98
-89 77 99 74 97
-90 78 75 97 98
-91 83 105 84 107
-92 103 82 84 108
-93 82 104 83 106
-94 101 86 108 87
-95 102 106 85 87
-96 100 85 107 86
-97 89 90 102 104
-98 88 100 90 105
-99 88 89 101 103
-100 113 117 96 98
-101 99 114 115 94
-102 112 116 95 97
-103 99 111 92 116
-104 93 117 97 109
-105 110 91 115 98
-106 110 114 93 95
-107 111 112 91 96
-108 113 92 94 109
-109 121 124 104 108
-110 122 125 105 106
-111 123 103 126 107
-112 102 124 107 118
-113 100 125 108 119
-114 101 126 106 120
-115 121 101 105 118
-116 122 102 103 119
-117 100 123 104 120
-118 112 115 128 129
-119 113 116 127 129
-120 114 127 117 128
-121 132 115 109 131
-122 110 132 116 130
-123 111 117 130 131
-124 112 134 135 109
-125 110 133 113 135
-126 111 133 134 114
-127 143 119 141 120
-128 144 139 118 120
-129 118 140 119 142
-130 122 144 123 137
-131 121 123 138 142
-132 121 143 122 136
-133 125 126 138 140
-134 124 136 126 141
-135 124 125 137 139
-136 132 134 149 153
-137 135 150 151 130
-138 133 148 152 131
-139 135 147 128 152
-140 133 145 129 153
-141 134 146 127 151
-142 146 150 129 131
-143 132 147 148 127
-144 145 149 128 130
-145 144 157 160 140
-146 158 161 141 142
-147 143 159 139 162
-148 143 154 138 160
-149 144 155 136 161
-150 156 137 162 142
-151 154 157 137 141
-152 155 158 138 139
-153 156 136 159 140
-154 165 148 151 164
-155 165 149 152 163
-156 150 163 153 164
-157 145 167 168 151
-158 166 146 168 152
-159 166 167 147 153
-160 145 148 170 171
-161 146 169 149 171
-162 147 169 170 150
-163 155 177 156 179
-164 154 156 180 175
-165 154 176 155 178
-166 158 180 159 173
-167 178 157 159 174
-168 157 179 158 172
-169 176 161 162 174
-170 177 160 172 162
-171 160 161 173 175
-172 189 168 170 185
-173 187 166 171 186
-174 188 167 169 184
-175 188 171 183 164
-176 165 189 169 181
-177 187 170 182 163
-178 165 167 182 186
-179 168 183 184 163
-180 166 181 185 164
-181 176 180 193 196
-182 177 178 194 197
-183 198 179 195 175
-184 179 190 174 196
-185 180 191 172 197
-186 198 178 192 173
-187 177 190 193 173
-188 191 194 174 175
-189 176 192 172 195
-190 187 200 201 184
-191 188 199 201 185
-192 199 189 200 186
-193 187 181 203 204
-194 188 202 182 204
-195 189 202 203 183
-196 181 184 206 207
-197 182 205 185 207
-198 183 205 206 186
-199 191 213 192 215
-200 211 190 192 216
-201 190 212 191 214
-202 209 194 216 195
-203 210 214 193 195
-204 193 215 194 208
-205 198 210 212 197
-206 198 213 196 208
-207 209 211 196 197
-208 5 204 206 9
-209 202 6 7 207
-210 4 203 205 8
-211 200 3 8 207
-212 1 201 205 9
-213 199 2 7 206
-214 2 201 203 6
-215 199 3 4 204
-216 1 200 202 5
0