Graph forms
for C4 [ 216, 99 ] = BGCG(UG(ATD[108,30]);K1;1)
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On this page are computer-accessible forms for the graph C4[ 216, 99 ] =
BGCG(UG(ATD[108,30]);K1;1).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {99, 114}, {103, 118}, {97, 114}, {108, 127}, {106, 127}, {107,
113}, {104, 117}, {108, 113}, {96, 126}, {78, 110}, {76, 109}, {95, 126}, {91,
121}, {90, 121}, {93, 121}, {95, 122}, {73, 110}, {87, 127}, {82, 121}, {85,
120}, {91, 118}, {95, 111}, {65, 112}, {94, 111}, {77, 120}, {68, 115}, {65,
120}, {86, 111}, {66, 120}, {65, 122}, {70, 123}, {48, 115}, {53, 114}, {61,
117}, {54, 125}, {48, 124}, {33, 110}, {42, 122}, {36, 118}, {40, 122}, {37,
119}, {34, 118}, {39, 114}, {34, 116}, {41, 112}, {46, 119}, {36, 126}, {42,
112}, {46, 115}, {13, 109}, {29, 125}, {21, 117}, {30, 125}, {21, 113}, {23,
115}, {19, 117}, {5, 109}, {4, 109}, {21, 127}, {16, 124}, {29, 113}, {17, 124},
{17, 126}, {31, 110}, {9, 125}, {12, 116}, {15, 119}, {2, 123}, {1, 123}, {14,
116}, {13, 119}, {7, 124}, {11, 112}, {17, 111}, {4, 123}, {11, 116}, {49, 177},
{57, 185}, {7, 134}, {56, 185}, {45, 172}, {78, 207}, {9, 139}, {52, 182}, {77,
207}, {24, 155}, {53, 182}, {35, 167}, {65, 197}, {6, 131}, {86, 211}, {51,
182}, {44, 169}, {64, 197}, {25, 159}, {34, 164}, {41, 174}, {27, 147}, {54,
190}, {77, 197}, {6, 143}, {92, 213}, {11, 129}, {25, 147}, {10, 129}, {42,
161}, {75, 192}, {7, 139}, {84, 216}, {59, 183}, {55, 186}, {94, 211}, {73,
196}, {9, 135}, {94, 208}, {18, 156}, {14, 129}, {38, 169}, {61, 178}, {43,
187}, {63, 175}, {12, 157}, {37, 180}, {31, 142}, {14, 159}, {8, 154}, {46,
188}, {13, 159}, {15, 156}, {84, 199}, {47, 188}, {39, 180}, {71, 212}, {18,
134}, {87, 195}, {92, 201}, {35, 181}, {92, 202}, {45, 187}, {17, 134}, {93,
202}, {34, 181}, {32, 183}, {52, 172}, {78, 214}, {82, 202}, {95, 198}, {29,
135}, {47, 181}, {1, 154}, {28, 135}, {2, 158}, {27, 135}, {58, 166}, {61, 161},
{72, 212}, {7, 154}, {83, 206}, {22, 139}, {49, 174}, {62, 161}, {63, 160}, {30,
190}, {33, 128}, {99, 194}, {51, 146}, {37, 132}, {60, 157}, {28, 190}, {55,
149}, {50, 144}, {38, 132}, {59, 153}, {40, 139}, {49, 146}, {56, 156}, {27,
190}, {20, 178}, {104, 206}, {47, 137}, {5, 162}, {98, 197}, {30, 185}, {21,
178}, {8, 175}, {5, 173}, {107, 195}, {26, 178}, {12, 164}, {62, 151}, {106,
195}, {103, 206}, {27, 177}, {99, 201}, {47, 133}, {35, 137}, {60, 150}, {18,
185}, {102, 205}, {101, 206}, {98, 201}, {55, 156}, {26, 177}, {23, 188}, {6,
170}, {52, 152}, {36, 137}, {101, 200}, {43, 134}, {4, 170}, {102, 200}, {56,
150}, {33, 143}, {10, 164}, {45, 130}, {8, 184}, {58, 138}, {1, 176}, {46, 159},
{20, 165}, {60, 141}, {61, 140}, {40, 154}, {44, 158}, {3, 176}, {96, 211}, {45,
158}, {63, 140}, {22, 162}, {97, 213}, {32, 148}, {26, 174}, {3, 182}, {48,
133}, {24, 173}, {23, 162}, {22, 163}, {10, 191}, {19, 165}, {100, 210}, {50,
132}, {38, 144}, {25, 174}, {98, 213}, {39, 144}, {58, 141}, {19, 170}, {57,
128}, {10, 176}, {41, 147}, {23, 173}, {57, 131}, {4, 191}, {44, 151}, {24,
163}, {3, 191}, {50, 142}, {20, 168}, {2, 191}, {26, 165}, {49, 142}, {1, 193},
{91, 155}, {20, 212}, {80, 144}, {68, 133}, {90, 155}, {105, 171}, {15, 204},
{104, 171}, {12, 200}, {19, 215}, {97, 164}, {16, 214}, {75, 141}, {92, 155},
{9, 193}, {107, 163}, {25, 209}, {64, 136}, {8, 193}, {107, 162}, {31, 214},
{71, 142}, {66, 136}, {79, 133}, {89, 149}, {94, 146}, {11, 198}, {104, 165},
{85, 152}, {86, 152}, {2, 205}, {90, 149}, {31, 208}, {81, 158}, {67, 147}, {83,
131}, {68, 148}, {6, 215}, {69, 148}, {5, 215}, {103, 181}, {91, 137}, {30,
204}, {24, 202}, {82, 128}, {96, 179}, {16, 196}, {88, 140}, {84, 128}, {69,
145}, {71, 146}, {87, 130}, {66, 148}, {108, 186}, {22, 193}, {106, 189}, {85,
130}, {84, 131}, {18, 203}, {13, 215}, {67, 153}, {77, 151}, {80, 138}, {3,
216}, {16, 203}, {66, 153}, {76, 151}, {81, 138}, {28, 192}, {83, 143}, {69,
153}, {82, 143}, {102, 187}, {89, 132}, {85, 136}, {15, 209}, {29, 195}, {28,
194}, {14, 209}, {108, 179}, {43, 203}, {106, 138}, {97, 129}, {53, 213}, {44,
205}, {70, 167}, {50, 208}, {88, 186}, {74, 168}, {51, 208}, {89, 186}, {64,
163}, {32, 196}, {75, 175}, {80, 180}, {33, 196}, {93, 184}, {74, 175}, {76,
169}, {43, 205}, {76, 170}, {78, 169}, {100, 140}, {38, 207}, {90, 179}, {73,
160}, {79, 166}, {81, 187}, {98, 136}, {75, 160}, {105, 130}, {88, 179}, {62,
210}, {81, 189}, {53, 216}, {89, 180}, {63, 210}, {64, 173}, {74, 167}, {39,
201}, {99, 141}, {54, 216}, {40, 198}, {69, 171}, {70, 168}, {72, 166}, {41,
198}, {71, 168}, {72, 167}, {56, 200}, {102, 150}, {54, 199}, {105, 152}, {62,
207}, {73, 184}, {67, 177}, {100, 150}, {74, 184}, {79, 189}, {52, 199}, {68,
183}, {79, 188}, {37, 209}, {101, 145}, {51, 199}, {67, 183}, {57, 204}, {96,
149}, {72, 189}, {32, 214}, {103, 145}, {70, 176}, {80, 166}, {35, 212}, {36,
211}, {42, 210}, {105, 145}, {101, 157}, {83, 171}, {58, 194}, {59, 194}, {100,
157}, {88, 161}, {86, 172}, {48, 203}, {87, 172}, {55, 204}, {59, 192}, {60,
192}, {93, 160} }>;
(II) A more general form is to represent the graph as the orbit of {99, 114}
under the group generated by the following permutations:
a: (1, 4, 13, 25, 49, 31, 16, 7)(2, 5, 14, 26, 50, 32, 17, 8)(3, 6, 15, 27, 51,
33, 18, 9)(10, 19, 37, 67, 94, 73, 43, 22)(11, 20, 38, 68, 95, 74, 44, 23)(12,
21, 39, 69, 96, 75, 45, 24)(28, 52, 82, 56, 29, 53, 83, 55)(30, 54, 84, 57)(34,
61, 80, 66, 36, 63, 81, 64)(35, 62, 79, 65)(40, 70, 76, 46, 41, 71, 78, 48)(42,
72, 77, 47)(58, 85, 91, 100, 106, 98, 103, 88)(59, 86, 93, 102, 107, 97, 104,
89)(60, 87, 92, 101, 108, 99, 105, 90)(109, 159, 174, 142, 214, 124, 154,
123)(110, 203, 139, 176, 170, 119, 147, 146)(111, 184, 205, 162, 129, 165, 132,
183)(112, 212, 207, 133, 122, 167, 151, 188)(113, 114, 171, 149, 192, 172, 202,
200)(115, 198, 168, 169)(116, 178, 144, 148, 126, 175, 158, 173)(117, 180, 153,
211, 160, 187, 163, 164)(118, 140, 138, 136)(120, 137, 210, 189, 197, 181, 161,
166)(121, 150, 195, 213, 206, 186, 194, 152)(125, 216, 131, 204, 190, 199, 128,
185)(127, 201, 145, 179, 141, 130, 155, 157)(134, 193, 191, 215, 209, 177, 208,
196)(135, 182, 143, 156) (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, 40, 3, 22)(4, 7, 10, 9)(5, 43, 11, 54)(6, 48, 12, 27)(8, 70)(13, 18, 14,
30)(16, 34, 28, 19)(17, 97, 29, 76)(20, 73, 35, 75)(21, 78, 36, 99)(23, 102, 41,
84)(24, 81, 42, 51)(25, 57, 46, 56)(26, 33, 47, 60)(31, 91, 58, 61)(32, 103, 59,
104)(37, 55)(38, 96, 39, 108)(44, 95, 53, 107)(45, 65, 52, 64)(49, 82, 79,
100)(50, 90, 80, 88)(62, 94, 92, 106)(63, 71, 93, 72)(66, 105)(67, 83, 68,
101)(77, 86, 98, 87)(109, 134, 129, 125)(110, 137, 141, 178)(111, 213, 195,
151)(112, 199, 173, 187)(113, 169, 126, 114)(115, 200, 147, 131)(116, 190, 215,
203)(117, 214, 118, 194)(119, 156, 209, 204)(120, 152, 136, 130)(121, 166, 140,
142)(122, 182, 163, 158)(123, 154, 176, 193)(124, 164, 135, 170)(127, 207, 211,
201)(128, 188, 150, 174)(132, 149, 180, 186)(133, 157, 177, 143)(138, 161, 208,
155)(139, 191)(144, 179)(145, 153, 171, 148)(146, 202, 189, 210)(159, 185)(160,
212)(162, 205, 198, 216)(165, 196, 181, 192)(167, 175, 168, 184)(172, 197)(183,
206)
c: (1, 2, 102, 101, 69, 67, 49, 50, 89, 90, 24, 22)(3, 81, 100, 83, 68, 41, 51,
80, 88, 82, 23, 40)(4, 43, 12, 105, 59, 26, 31, 37, 96, 92, 107, 8)(5, 7, 10,
45, 60, 104, 32, 25, 94, 39, 108, 93)(6, 48, 11, 52, 58, 61, 33, 46, 95, 53,
106, 63)(9, 70, 44, 56, 103, 66, 27, 71, 38, 55, 91, 64)(13, 17, 97, 87, 75, 19,
16, 14, 86, 99, 21, 73)(15, 36, 98, 29, 74, 76, 18, 34, 85, 28, 20, 78)(30, 35,
77)(42, 84, 79)(47, 65, 54, 72, 62, 57)(109, 134, 164, 130, 192, 165, 214, 209,
211, 201, 113, 184)(110, 119, 126, 213, 195, 175, 170, 203, 116, 152, 194,
178)(111, 114, 127, 160, 215, 124, 129, 172, 141, 117, 196, 159)(112, 199, 166,
161, 128, 188, 122, 216, 189, 210, 131, 133)(115, 198, 182, 138, 140, 143)(118,
136, 135, 168, 169, 156)(120, 190, 212, 207, 204, 137, 197, 125, 167, 151, 185,
181)(121, 173, 139, 176, 158, 150, 206, 148, 147, 146, 144, 186)(123, 205, 200,
145, 153, 177, 142, 132, 149, 155, 163, 193)(154, 191, 187, 157, 171, 183, 174,
208, 180, 179, 202, 162)
d: (2, 3)(4, 10)(5, 11)(6, 12)(7, 9)(13, 14)(16, 28)(17, 29)(18, 30)(19, 34)(20,
35)(21, 36)(22, 40)(23, 41)(24, 42)(25, 46)(26, 47)(27, 48)(31, 58)(32, 59)(33,
60)(38, 39)(43, 54)(44, 53)(45, 52)(49, 79)(50, 80)(51, 81)(56, 57)(61, 91)(62,
92)(63, 93)(64, 65)(67, 68)(71, 72)(73, 75)(76, 97)(77, 98)(78, 99)(82, 100)(83,
101)(84, 102)(86, 87)(88, 90)(94, 106)(95, 107)(96, 108)(103, 104)(109,
129)(110, 141)(111, 195)(112, 173)(113, 126)(114, 169)(115, 147)(116, 215)(117,
118)(119, 209)(120, 136)(121, 140)(122, 163)(123, 176)(124, 135)(125, 134)(127,
211)(128, 150)(130, 152)(131, 200)(132, 180)(133, 177)(137, 178)(138, 208)(142,
166)(143, 157)(145, 171)(146, 189)(148, 153)(149, 186)(151, 213)(154, 193)(155,
161)(156, 204)(158, 182)(162, 198)(164, 170)(165, 181)(167, 168)(174, 188)(175,
184)(187, 199)(190, 203)(192, 196)(194, 214)(201, 207)(202, 210)(205, 216)
C4[ 216, 99 ]
216
-1 154 176 123 193
-2 123 158 191 205
-3 176 191 182 216
-4 123 191 170 109
-5 215 162 173 109
-6 143 170 215 131
-7 154 134 124 139
-8 154 193 184 175
-9 135 125 193 139
-10 176 191 129 164
-11 198 112 116 129
-12 200 157 116 164
-13 159 215 119 109
-14 209 159 116 129
-15 209 156 204 119
-16 124 203 214 196
-17 111 134 124 126
-18 134 156 203 185
-19 165 170 215 117
-20 165 178 168 212
-21 178 113 127 117
-22 193 139 162 163
-23 188 115 162 173
-24 155 202 173 163
-25 209 147 159 174
-26 165 177 178 174
-27 177 135 190 147
-28 135 190 192 194
-29 113 135 125 195
-30 190 125 204 185
-31 110 214 142 208
-32 148 214 183 196
-33 110 143 128 196
-34 181 116 118 164
-35 167 212 137 181
-36 211 126 137 118
-37 132 209 180 119
-38 132 144 169 207
-39 144 201 114 180
-40 154 198 122 139
-41 198 112 147 174
-42 122 210 112 161
-43 187 134 203 205
-44 158 169 205 151
-45 187 158 172 130
-46 188 115 159 119
-47 133 188 137 181
-48 133 124 115 203
-49 177 146 174 142
-50 132 144 142 208
-51 199 146 182 208
-52 199 182 172 152
-53 114 213 182 216
-54 199 190 125 216
-55 156 149 204 186
-56 156 200 150 185
-57 204 128 185 131
-58 166 138 194 141
-59 192 183 194 153
-60 157 192 150 141
-61 178 117 161 140
-62 210 161 151 207
-63 210 160 140 175
-64 136 173 163 197
-65 122 112 120 197
-66 136 148 120 153
-67 177 147 183 153
-68 133 115 148 183
-69 145 148 171 153
-70 176 123 167 168
-71 146 168 212 142
-72 166 167 189 212
-73 110 160 184 196
-74 167 168 184 175
-75 192 160 141 175
-76 169 170 151 109
-77 151 207 120 197
-78 110 169 214 207
-79 133 166 188 189
-80 144 166 180 138
-81 187 189 158 138
-82 121 143 202 128
-83 143 171 206 131
-84 199 128 216 131
-85 136 130 152 120
-86 111 211 172 152
-87 127 172 195 130
-88 179 161 140 186
-89 132 180 149 186
-90 121 155 179 149
-91 121 155 137 118
-92 155 201 202 213
-93 121 202 160 184
-94 111 211 146 208
-95 198 111 122 126
-96 211 179 126 149
-97 114 213 129 164
-98 201 136 213 197
-99 201 114 194 141
-100 210 157 150 140
-101 145 200 157 206
-102 187 200 150 205
-103 145 181 118 206
-104 165 171 117 206
-105 145 171 130 152
-106 189 127 138 195
-107 113 162 195 163
-108 113 179 127 186
-109 13 4 5 76
-110 33 78 73 31
-111 17 94 95 86
-112 11 41 42 65
-113 29 107 108 21
-114 99 39 53 97
-115 23 46 68 48
-116 11 12 34 14
-117 104 61 19 21
-118 34 36 91 103
-119 13 46 15 37
-120 66 77 85 65
-121 90 91 82 93
-122 40 95 42 65
-123 1 2 4 70
-124 48 16 17 7
-125 29 30 9 54
-126 36 17 95 96
-127 106 108 21 87
-128 33 57 82 84
-129 11 14 97 10
-130 45 105 85 87
-131 57 6 83 84
-132 89 37 38 50
-133 68 79 47 48
-134 17 7 18 43
-135 27 28 29 9
-136 66 85 64 98
-137 35 36 47 91
-138 58 80 81 106
-139 22 7 40 9
-140 88 100 61 63
-141 99 58 60 75
-142 49 71 50 31
-143 33 82 6 83
-144 80 38 39 50
-145 101 69 103 105
-146 49 71 94 51
-147 67 25 27 41
-148 66 68 69 32
-149 55 89 90 96
-150 56 100 102 60
-151 44 77 62 76
-152 105 52 85 86
-153 66 67 69 59
-154 1 7 40 8
-155 24 90 91 92
-156 55 56 15 18
-157 12 100 101 60
-158 44 45 2 81
-159 13 46 14 25
-160 93 73 63 75
-161 88 61 62 42
-162 22 23 5 107
-163 22 24 107 64
-164 12 34 97 10
-165 26 104 19 20
-166 79 58 80 72
-167 35 70 72 74
-168 70 71 74 20
-169 44 78 38 76
-170 4 6 19 76
-171 69 104 83 105
-172 45 52 86 87
-173 23 24 5 64
-174 25 26 49 41
-175 8 63 74 75
-176 1 3 70 10
-177 67 26 27 49
-178 26 61 20 21
-179 88 90 96 108
-180 89 80 37 39
-181 34 35 47 103
-182 3 51 52 53
-183 67 68 59 32
-184 93 73 8 74
-185 56 57 18 30
-186 55 88 89 108
-187 45 102 81 43
-188 23 46 79 47
-189 79 81 72 106
-190 27 28 30 54
-191 2 3 4 10
-192 59 60 28 75
-193 22 1 8 9
-194 99 58 59 28
-195 29 106 107 87
-196 33 16 73 32
-197 77 64 65 98
-198 11 40 95 41
-199 51 84 52 54
-200 12 56 101 102
-201 99 92 39 98
-202 24 92 82 93
-203 48 16 18 43
-204 55 57 15 30
-205 44 2 102 43
-206 101 103 104 83
-207 77 78 38 62
-208 50 94 51 31
-209 14 25 15 37
-210 100 62 63 42
-211 36 94 96 86
-212 35 71 72 20
-213 92 53 97 98
-214 78 16 31 32
-215 13 5 6 19
-216 3 84 53 54
0