Graph forms
for C4 [ 216, 96 ] =
BGCG(AMC(3,12,[1.1:9.10]);K1;3)
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On this page are computer-accessible forms for the graph C4[ 216, 96 ] =
BGCG(AMC(3,12,[1.1:9.10]);K1;3).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {106, 111}, {98, 111}, {99, 110}, {105, 120}, {104, 122}, {107,
121}, {97, 118}, {98, 123}, {96, 123}, {96, 124}, {105, 117}, {101, 120}, {97,
127}, {100, 122}, {105, 118}, {93, 127}, {94, 125}, {84, 112}, {88, 124}, {87,
115}, {89, 126}, {90, 125}, {93, 119}, {89, 119}, {81, 126}, {64, 114}, {95,
109}, {75, 121}, {68, 112}, {91, 110}, {65, 121}, {77, 117}, {74, 112}, {87,
109}, {72, 116}, {79, 115}, {70, 120}, {69, 122}, {58, 122}, {62, 127}, {49,
114}, {59, 120}, {53, 113}, {59, 125}, {51, 127}, {48, 125}, {58, 119}, {33,
111}, {62, 113}, {40, 121}, {32, 118}, {35, 117}, {47, 119}, {45, 116}, {43,
112}, {19, 114}, {25, 123}, {23, 113}, {23, 124}, {26, 113}, {27, 118}, {16,
126}, {28, 114}, {18, 124}, {20, 123}, {4, 117}, {6, 116}, {28, 111}, {26, 110},
{11, 126}, {9, 115}, {21, 110}, {22, 109}, {17, 109}, {9, 116}, {14, 115}, {1,
128}, {45, 172}, {39, 166}, {4, 133}, {59, 186}, {74, 203}, {7, 133}, {50, 176},
{37, 167}, {36, 166}, {8, 138}, {24, 155}, {85, 214}, {84, 215}, {82, 209}, {25,
154}, {81, 210}, {47, 171}, {51, 183}, {48, 180}, {63, 187}, {65, 197}, {7,
130}, {83, 214}, {46, 168}, {57, 191}, {6, 129}, {27, 156}, {13, 138}, {58,
189}, {63, 184}, {67, 196}, {25, 145}, {93, 213}, {40, 160}, {71, 207}, {15,
134}, {44, 165}, {40, 161}, {38, 175}, {31, 150}, {20, 158}, {46, 164}, {54,
188}, {74, 192}, {76, 198}, {2, 137}, {53, 190}, {33, 170}, {24, 147}, {20,
159}, {12, 135}, {64, 203}, {10, 134}, {35, 175}, {22, 154}, {15, 131}, {12,
128}, {54, 187}, {59, 182}, {61, 176}, {73, 196}, {29, 147}, {30, 144}, {64,
206}, {71, 201}, {17, 158}, {95, 208}, {72, 199}, {6, 150}, {51, 163}, {15,
159}, {5, 148}, {95, 206}, {92, 205}, {46, 191}, {36, 181}, {34, 179}, {11,
153}, {88, 202}, {25, 139}, {16, 130}, {55, 165}, {51, 160}, {80, 195}, {71,
211}, {77, 216}, {13, 155}, {37, 179}, {17, 135}, {60, 170}, {14, 153}, {90,
205}, {83, 196}, {10, 146}, {38, 190}, {37, 188}, {90, 195}, {62, 167}, {72,
209}, {32, 186}, {44, 182}, {24, 131}, {41, 178}, {73, 210}, {76, 215}, {61,
161}, {42, 183}, {38, 184}, {84, 202}, {13, 146}, {78, 209}, {11, 171}, {33,
129}, {27, 187}, {23, 182}, {106, 203}, {99, 194}, {28, 189}, {10, 168}, {31,
189}, {24, 187}, {49, 146}, {39, 132}, {3, 166}, {4, 161}, {56, 157}, {57, 156},
{55, 145}, {97, 199}, {56, 158}, {9, 174}, {41, 142}, {37, 130}, {29, 186}, {10,
173}, {61, 154}, {5, 173}, {33, 137}, {1, 168}, {107, 194}, {16, 185}, {2, 171},
{60, 149}, {4, 174}, {62, 148}, {42, 129}, {50, 153}, {21, 185}, {108, 192},
{107, 199}, {2, 175}, {99, 206}, {43, 133}, {104, 198}, {52, 154}, {45, 131},
{54, 152}, {17, 190}, {36, 139}, {5, 181}, {101, 213}, {45, 157}, {41, 153},
{47, 158}, {97, 208}, {1, 179}, {2, 177}, {35, 144}, {34, 145}, {26, 169}, {63,
140}, {22, 162}, {32, 148}, {30, 170}, {57, 141}, {102, 211}, {7, 177}, {52,
130}, {50, 132}, {31, 169}, {21, 163}, {8, 190}, {3, 180}, {56, 143}, {12, 180},
{52, 140}, {36, 156}, {15, 183}, {14, 182}, {27, 162}, {106, 211}, {49, 136},
{40, 146}, {52, 142}, {12, 183}, {44, 151}, {30, 163}, {41, 148}, {31, 161},
{43, 149}, {63, 129}, {60, 131}, {103, 216}, {85, 149}, {91, 155}, {1, 192},
{104, 169}, {23, 213}, {93, 159}, {89, 155}, {75, 137}, {14, 205}, {19, 208},
{70, 133}, {18, 214}, {3, 198}, {96, 165}, {13, 200}, {18, 212}, {100, 162},
{91, 157}, {8, 207}, {28, 213}, {68, 141}, {5, 207}, {95, 149}, {87, 157}, {85,
159}, {66, 136}, {67, 143}, {77, 128}, {94, 147}, {30, 208}, {79, 128}, {104,
167}, {102, 169}, {3, 210}, {105, 184}, {85, 132}, {20, 197}, {7, 214}, {6,
215}, {69, 151}, {94, 140}, {18, 193}, {91, 136}, {26, 201}, {21, 193}, {72,
156}, {81, 132}, {82, 135}, {80, 134}, {102, 176}, {70, 145}, {29, 197}, {79,
151}, {65, 152}, {87, 142}, {8, 210}, {11, 215}, {86, 138}, {16, 204}, {75,
151}, {9, 212}, {90, 135}, {83, 142}, {19, 205}, {108, 178}, {88, 134}, {84,
138}, {22, 200}, {19, 204}, {106, 181}, {29, 194}, {73, 150}, {32, 192}, {42,
202}, {34, 194}, {76, 172}, {66, 163}, {80, 177}, {46, 204}, {54, 212}, {43,
200}, {108, 143}, {92, 191}, {44, 207}, {71, 164}, {34, 198}, {66, 166}, {74,
174}, {38, 195}, {89, 188}, {61, 216}, {75, 173}, {88, 191}, {94, 185}, {77,
164}, {78, 167}, {35, 201}, {103, 141}, {70, 172}, {67, 168}, {39, 203}, {103,
139}, {92, 176}, {98, 143}, {101, 136}, {65, 175}, {103, 137}, {101, 139}, {99,
141}, {98, 140}, {60, 211}, {86, 185}, {68, 171}, {69, 170}, {55, 199}, {66,
178}, {48, 193}, {56, 201}, {69, 180}, {73, 184}, {42, 216}, {82, 160}, {49,
195}, {58, 200}, {39, 212}, {86, 165}, {64, 179}, {79, 188}, {48, 196}, {100,
144}, {81, 164}, {102, 147}, {86, 160}, {50, 197}, {57, 193}, {96, 152}, {53,
206}, {55, 204}, {78, 181}, {80, 172}, {108, 144}, {100, 152}, {82, 174}, {107,
150}, {47, 209}, {92, 162}, {83, 173}, {67, 189}, {68, 186}, {76, 178}, {53,
202}, {78, 177} }>;
(II) A more general form is to represent the graph as the orbit of {106, 111}
under the group generated by the following permutations:
a: (1, 2)(3, 6)(4, 5)(7, 32)(8, 31)(9, 36)(10, 35)(11, 34)(12, 33)(13, 26)(14,
25)(15, 30)(16, 29)(17, 28)(18, 27)(19, 20)(21, 24)(22, 23)(37, 68)(38, 67)(39,
72)(40, 71)(41, 70)(42, 69)(43, 62)(44, 61)(45, 66)(46, 65)(47, 64)(48, 63)(49,
56)(50, 55)(51, 60)(52, 59)(53, 58)(54, 57)(74, 78)(75, 77)(79, 103)(80,
108)(81, 107)(82, 106)(83, 105)(84, 104)(85, 97)(86, 102)(87, 101)(88, 100)(89,
99)(90, 98)(92, 96)(93, 95)(109, 213)(110, 155)(111, 135)(112, 167)(113,
200)(114, 158)(115, 139)(116, 166)(117, 173)(118, 214)(119, 206)(120, 142)(121,
164)(122, 202)(123, 205)(124, 162)(125, 140)(126, 194)(127, 149)(128, 137)(129,
180)(130, 186)(131, 163)(132, 199)(133, 148)(134, 144)(136, 157)(138, 169)(141,
188)(143, 195)(145, 153)(146, 201)(147, 185)(150, 210)(151, 216)(152, 191)(154,
182)(156, 212)(159, 208)(160, 211)(161, 207)(165, 176)(168, 175)(170, 183)(171,
179)(172, 178)(174, 181)(177, 192)(184, 196)(187, 193)(189, 190)(197, 204)(198,
215)(203, 209) (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, 37, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67)(2, 60, 8, 66, 14, 72, 20, 42,
26, 48, 32, 54)(3, 41, 9, 47, 15, 53, 21, 59, 27, 65, 33, 71)(4, 58, 10, 64, 16,
70, 22, 40, 28, 46, 34, 52)(5, 39, 11, 45, 17, 51, 23, 57, 29, 63, 35, 69)(6,
56, 12, 62, 18, 68, 24, 38, 30, 44, 36, 50)(73, 108, 79, 78, 85, 84, 91, 90, 97,
96, 103, 102)(74, 89, 80, 95, 86, 101, 92, 107, 98, 77, 104, 83)(75, 106, 81,
76, 87, 82, 93, 88, 99, 94, 105, 100)(109, 160, 213, 191, 194, 140, 117, 122,
173, 203, 126, 172)(110, 125, 118, 152, 137, 211, 210, 178, 115, 209, 159,
202)(111, 164, 198, 142, 174, 119, 134, 206, 185, 120, 162, 121)(112, 155, 195,
208, 165, 139, 176, 150, 143, 128, 167, 214)(113, 193, 186, 187, 175, 170, 207,
166, 153, 116, 158, 183)(114, 204, 145, 154, 161, 189, 168, 179, 130, 133, 200,
146)(123, 216, 169, 196, 192, 188, 177, 149, 138, 136, 205, 199)(124, 141, 147,
184, 144, 151, 181, 132, 215, 157, 135, 127)(129, 201, 180, 148, 212, 171, 131,
190, 163, 182, 156, 197)
c: (2, 6)(3, 5)(7, 31)(8, 36)(9, 35)(10, 34)(11, 33)(12, 32)(13, 25)(14, 30)(15,
29)(16, 28)(17, 27)(18, 26)(20, 24)(21, 23)(37, 67)(38, 72)(39, 71)(40, 70)(41,
69)(42, 68)(43, 61)(44, 66)(45, 65)(46, 64)(47, 63)(48, 62)(49, 55)(50, 60)(51,
59)(52, 58)(53, 57)(54, 56)(73, 78)(74, 77)(75, 76)(79, 108)(80, 107)(81,
106)(82, 105)(83, 104)(84, 103)(85, 102)(86, 101)(87, 100)(88, 99)(89, 98)(90,
97)(91, 96)(92, 95)(93, 94)(109, 162)(110, 124)(111, 126)(112, 216)(113,
193)(114, 204)(115, 144)(116, 175)(117, 174)(118, 135)(119, 140)(120, 160)(121,
172)(122, 142)(123, 155)(125, 127)(128, 192)(129, 171)(130, 189)(131, 197)(132,
211)(133, 161)(134, 194)(136, 165)(137, 215)(138, 139)(141, 202)(143, 188)(145,
146)(147, 159)(148, 180)(149, 176)(150, 177)(151, 178)(152, 157)(153, 170)(154,
200)(156, 190)(158, 187)(163, 182)(164, 203)(166, 207)(167, 196)(168, 179)(169,
214)(173, 198)(181, 210)(183, 186)(184, 209)(185, 213)(191, 206)(195, 199)(201,
212)(205, 208)
d: (2, 23)(4, 19)(6, 21)(7, 14)(8, 36)(9, 16)(10, 32)(11, 18)(12, 34)(13,
27)(15, 29)(17, 25)(26, 33)(28, 35)(30, 31)(37, 79)(38, 101)(39, 81)(40, 97)(41,
83)(42, 99)(43, 92)(44, 78)(45, 94)(46, 74)(47, 96)(48, 76)(49, 105)(50, 85)(51,
107)(52, 87)(53, 103)(54, 89)(55, 82)(56, 98)(57, 84)(58, 100)(59, 80)(60,
102)(61, 95)(62, 75)(63, 91)(64, 77)(65, 93)(66, 73)(67, 108)(68, 88)(69,
104)(70, 90)(71, 106)(72, 86)(109, 154)(110, 129)(111, 201)(112, 191)(113,
137)(114, 117)(115, 130)(116, 185)(118, 146)(119, 152)(120, 195)(121, 127)(123,
158)(124, 171)(125, 172)(126, 212)(128, 179)(131, 147)(133, 205)(134, 186)(135,
145)(136, 184)(138, 156)(139, 190)(140, 157)(141, 202)(144, 189)(148, 173)(149,
176)(150, 163)(151, 167)(153, 214)(155, 187)(159, 197)(160, 199)(161, 208)(162,
200)(164, 203)(165, 209)(166, 210)(168, 192)(169, 170)(174, 204)(175, 213)(177,
182)(178, 196)(180, 198)(181, 207)(183, 194)(193, 215)(206, 216)
e: (1, 7)(2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(13, 31)(14, 36)(15, 35)(16, 34)(17,
33)(18, 32)(19, 25)(20, 30)(21, 29)(22, 28)(23, 27)(24, 26)(38, 42)(39, 41)(43,
67)(44, 72)(45, 71)(46, 70)(47, 69)(48, 68)(49, 61)(50, 66)(51, 65)(52, 64)(53,
63)(54, 62)(56, 60)(57, 59)(73, 84)(74, 83)(75, 82)(76, 81)(77, 80)(78, 79)(85,
108)(86, 107)(87, 106)(88, 105)(89, 104)(90, 103)(91, 102)(92, 101)(93, 100)(94,
99)(95, 98)(96, 97)(109, 111)(110, 147)(112, 196)(113, 187)(114, 154)(115,
181)(116, 207)(117, 134)(118, 124)(119, 122)(120, 191)(121, 160)(123, 208)(125,
141)(126, 198)(127, 152)(128, 177)(129, 190)(130, 179)(131, 201)(132, 178)(133,
168)(135, 137)(136, 176)(138, 150)(139, 205)(140, 206)(142, 203)(143, 149)(144,
159)(145, 204)(146, 161)(148, 212)(151, 209)(153, 166)(155, 169)(156, 182)(157,
211)(158, 170)(162, 213)(163, 197)(164, 172)(165, 199)(167, 188)(171, 180)(173,
174)(175, 183)(184, 202)(185, 194)(186, 193)(189, 200)(192, 214)(195, 216)(210,
215)
C4[ 216, 96 ]
216
-1 168 179 192 128
-2 177 137 171 175
-3 198 166 210 180
-4 133 117 161 174
-5 148 181 173 207
-6 116 215 150 129
-7 133 177 214 130
-8 210 190 138 207
-9 212 115 116 174
-10 134 146 168 173
-11 126 171 215 153
-12 135 180 128 183
-13 155 200 146 138
-14 115 182 205 153
-15 134 159 183 131
-16 126 204 130 185
-17 135 190 158 109
-18 124 212 214 193
-19 114 204 205 208
-20 123 158 159 197
-21 110 193 163 185
-22 154 200 162 109
-23 113 124 213 182
-24 187 155 147 131
-25 154 123 145 139
-26 110 113 201 169
-27 187 156 118 162
-28 111 189 114 213
-29 147 194 186 197
-30 144 170 163 208
-31 189 169 150 161
-32 148 192 118 186
-33 111 137 170 129
-34 198 145 179 194
-35 144 201 117 175
-36 166 156 181 139
-37 188 167 179 130
-38 190 184 195 175
-39 132 166 212 203
-40 121 146 160 161
-41 178 148 142 153
-42 202 183 216 129
-43 133 112 200 149
-44 165 182 151 207
-45 157 116 172 131
-46 168 191 204 164
-47 209 158 171 119
-48 125 180 193 196
-49 146 114 136 195
-50 132 176 153 197
-51 127 160 183 163
-52 154 140 130 142
-53 113 190 202 206
-54 187 188 212 152
-55 165 199 145 204
-56 143 157 201 158
-57 156 191 193 141
-58 122 189 200 119
-59 125 182 120 186
-60 211 170 149 131
-61 154 176 161 216
-62 167 113 148 127
-63 187 129 140 184
-64 179 114 203 206
-65 121 152 175 197
-66 166 178 136 163
-67 143 189 168 196
-68 112 171 141 186
-69 122 180 170 151
-70 133 145 172 120
-71 211 201 207 164
-72 209 199 156 116
-73 210 150 184 196
-74 112 192 203 174
-75 121 137 151 173
-76 198 178 215 172
-77 117 128 216 164
-78 209 177 167 181
-79 188 115 128 151
-80 177 134 172 195
-81 132 210 126 164
-82 209 135 160 174
-83 214 173 196 142
-84 112 202 138 215
-85 132 159 214 149
-86 165 138 160 185
-87 157 115 109 142
-88 134 124 191 202
-89 155 188 126 119
-90 135 125 205 195
-91 110 155 157 136
-92 176 191 205 162
-93 213 159 127 119
-94 125 147 140 185
-95 149 206 109 208
-96 165 123 124 152
-97 199 127 118 208
-98 143 111 123 140
-99 110 194 206 141
-100 122 144 162 152
-101 136 213 139 120
-102 176 211 147 169
-103 137 139 216 141
-104 198 122 167 169
-105 117 118 184 120
-106 111 211 181 203
-107 121 199 150 194
-108 143 144 178 192
-109 22 17 95 87
-110 99 91 26 21
-111 33 28 106 98
-112 68 84 74 43
-113 23 26 62 53
-114 49 28 19 64
-115 79 14 9 87
-116 45 6 72 9
-117 77 35 4 105
-118 27 105 97 32
-119 89 47 58 93
-120 101 59 70 105
-121 40 107 75 65
-122 100 58 69 104
-123 25 96 20 98
-124 88 23 18 96
-125 90 48 59 94
-126 11 89 81 16
-127 93 51 62 97
-128 77 1 12 79
-129 33 6 63 42
-130 37 16 7 52
-131 45 24 15 60
-132 81 39 50 85
-133 4 70 7 43
-134 88 80 15 10
-135 12 90 82 17
-136 66 101 91 49
-137 33 2 103 75
-138 13 84 8 86
-139 101 25 36 103
-140 94 52 63 98
-141 99 57 68 103
-142 83 41 52 87
-143 56 67 108 98
-144 100 35 30 108
-145 55 34 25 70
-146 13 49 40 10
-147 24 102 94 29
-148 5 62 41 32
-149 60 95 85 43
-150 6 73 107 31
-151 44 79 69 75
-152 100 96 54 65
-153 11 14 50 41
-154 22 25 61 52
-155 89 13 24 91
-156 57 36 27 72
-157 45 56 91 87
-158 56 47 17 20
-159 15 93 85 20
-160 82 40 51 86
-161 4 61 40 31
-162 22 100 92 27
-163 66 51 30 21
-164 77 46 81 71
-165 44 55 96 86
-166 66 3 36 39
-167 78 37 104 62
-168 1 67 46 10
-169 102 26 104 31
-170 33 69 60 30
-171 11 2 68 47
-172 45 80 70 76
-173 5 83 75 10
-174 4 82 74 9
-175 2 35 38 65
-176 102 92 50 61
-177 78 2 80 7
-178 66 41 108 76
-179 1 34 37 64
-180 12 3 69 48
-181 78 36 5 106
-182 44 23 14 59
-183 12 15 51 42
-184 38 105 73 63
-185 16 94 86 21
-186 68 59 29 32
-187 24 27 63 54
-188 89 79 37 54
-189 67 58 28 31
-190 38 17 8 53
-191 88 46 57 92
-192 1 74 108 32
-193 57 48 18 21
-194 99 34 29 107
-195 90 80 38 49
-196 67 48 83 73
-197 50 29 20 65
-198 34 3 104 76
-199 55 72 107 97
-200 22 13 58 43
-201 56 35 26 71
-202 88 84 42 53
-203 39 106 74 64
-204 55 46 16 19
-205 90 14 92 19
-206 99 95 53 64
-207 44 5 71 8
-208 95 19 30 97
-209 78 47 82 72
-210 3 81 73 8
-211 102 60 71 106
-212 39 18 9 54
-213 23 101 93 28
-214 83 7 18 85
-215 11 6 84 76
-216 77 103 61 42
0