Graph forms
for C4 [ 216, 83 ] =
PL(CS(AMC(3,3,[0.1:2.2])[3^18],0))
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On this page are computer-accessible forms for the graph C4[ 216, 83 ] =
PL(CS(AMC(3,3,[0.1:2.2])[3^18],0)).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {107, 120}, {108, 120}, {106, 115}, {105, 115}, {108, 118}, {96,
124}, {105, 117}, {98, 127}, {107, 118}, {96, 126}, {97, 127}, {106, 117}, {95,
126}, {95, 124}, {93, 121}, {94, 123}, {93, 123}, {94, 121}, {91, 114}, {91,
112}, {92, 112}, {92, 114}, {89, 109}, {90, 111}, {89, 111}, {64, 119}, {90,
109}, {64, 120}, {51, 114}, {51, 113}, {52, 113}, {56, 125}, {52, 114}, {56,
126}, {63, 120}, {61, 117}, {63, 119}, {55, 126}, {61, 116}, {55, 125}, {62,
116}, {62, 117}, {54, 122}, {54, 123}, {53, 123}, {53, 122}, {50, 110}, {50,
111}, {49, 111}, {49, 110}, {1, 109}, {2, 110}, {1, 110}, {2, 109}, {3, 115},
{2, 115}, {3, 113}, {4, 118}, {3, 112}, {4, 119}, {4, 112}, {8, 124}, {4, 113},
{8, 125}, {1, 119}, {2, 116}, {1, 118}, {3, 116}, {7, 127}, {6, 127}, {7, 125},
{7, 124}, {5, 121}, {6, 122}, {5, 122}, {6, 121}, {11, 139}, {10, 139}, {89,
216}, {47, 174}, {11, 137}, {47, 173}, {12, 142}, {11, 136}, {12, 143}, {12,
136}, {92, 216}, {46, 170}, {16, 148}, {75, 207}, {12, 137}, {46, 171}, {16,
149}, {74, 207}, {5, 131}, {45, 171}, {10, 140}, {9, 143}, {6, 128}, {75, 205},
{5, 130}, {45, 170}, {11, 140}, {9, 142}, {7, 128}, {74, 205}, {91, 211}, {43,
162}, {90, 211}, {8, 130}, {92, 214}, {43, 161}, {16, 154}, {8, 131}, {52, 191},
{16, 155}, {9, 133}, {18, 158}, {17, 157}, {10, 134}, {44, 161}, {44, 162}, {91,
213}, {51, 189}, {50, 188}, {49, 191}, {9, 134}, {90, 213}, {89, 214}, {51,
188}, {50, 189}, {18, 157}, {17, 158}, {10, 133}, {38, 182}, {87, 199}, {84,
196}, {83, 195}, {39, 183}, {38, 183}, {86, 199}, {82, 195}, {40, 185}, {39,
182}, {40, 186}, {88, 202}, {84, 198}, {83, 193}, {82, 193}, {88, 204}, {81,
196}, {13, 155}, {14, 152}, {13, 154}, {81, 198}, {15, 152}, {15, 151}, {14,
151}, {85, 204}, {73, 208}, {15, 149}, {15, 148}, {73, 210}, {13, 145}, {37,
185}, {14, 146}, {76, 208}, {48, 173}, {93, 192}, {48, 174}, {87, 201}, {76,
210}, {13, 146}, {86, 201}, {85, 202}, {37, 186}, {14, 145}, {27, 187}, {96,
192}, {26, 187}, {61, 156}, {27, 185}, {28, 190}, {27, 184}, {28, 191}, {28,
184}, {28, 185}, {21, 179}, {26, 188}, {25, 191}, {22, 176}, {61, 155}, {62,
152}, {63, 153}, {21, 178}, {27, 188}, {25, 190}, {23, 176}, {62, 153}, {63,
152}, {24, 178}, {24, 179}, {25, 181}, {26, 182}, {25, 182}, {26, 181}, {19,
163}, {18, 163}, {39, 150}, {59, 138}, {19, 161}, {39, 149}, {20, 166}, {59,
137}, {19, 160}, {20, 167}, {20, 160}, {42, 158}, {38, 146}, {24, 172}, {20,
161}, {42, 159}, {38, 147}, {24, 173}, {60, 137}, {17, 167}, {41, 159}, {37,
147}, {18, 164}, {60, 138}, {17, 166}, {41, 158}, {37, 146}, {19, 164}, {23,
175}, {22, 175}, {23, 173}, {23, 172}, {21, 169}, {22, 170}, {58, 134}, {40,
149}, {58, 135}, {40, 150}, {57, 135}, {21, 170}, {22, 169}, {57, 134}, {65,
129}, {84, 148}, {81, 145}, {67, 131}, {68, 132}, {65, 128}, {105, 168}, {82,
147}, {66, 128}, {84, 150}, {81, 147}, {66, 129}, {82, 145}, {108, 168}, {83,
150}, {67, 132}, {83, 148}, {68, 131}, {72, 143}, {69, 141}, {107, 163}, {71,
143}, {69, 140}, {106, 163}, {70, 140}, {108, 166}, {70, 141}, {99, 175}, {98,
175}, {107, 165}, {105, 166}, {106, 165}, {85, 133}, {100, 180}, {88, 136}, {86,
135}, {85, 135}, {99, 177}, {88, 138}, {86, 133}, {98, 177}, {97, 178}, {73,
157}, {74, 159}, {97, 180}, {29, 203}, {100, 178}, {30, 200}, {73, 159}, {29,
202}, {31, 200}, {71, 144}, {74, 157}, {31, 199}, {72, 144}, {30, 199}, {31,
197}, {31, 196}, {64, 155}, {29, 193}, {30, 194}, {64, 156}, {87, 138}, {96,
190}, {29, 194}, {87, 136}, {30, 193}, {46, 206}, {100, 132}, {97, 129}, {47,
207}, {46, 207}, {99, 130}, {79, 174}, {48, 209}, {47, 206}, {57, 216}, {48,
210}, {95, 189}, {68, 167}, {98, 129}, {94, 189}, {93, 190}, {79, 172}, {32,
196}, {95, 187}, {60, 216}, {77, 169}, {32, 197}, {94, 187}, {78, 171}, {65,
167}, {104, 142}, {100, 130}, {66, 164}, {67, 165}, {77, 171}, {66, 165}, {99,
132}, {67, 164}, {78, 169}, {42, 194}, {101, 141}, {80, 184}, {43, 195}, {42,
195}, {103, 142}, {44, 197}, {43, 194}, {65, 168}, {75, 162}, {32, 202}, {80,
186}, {44, 198}, {32, 203}, {102, 141}, {60, 215}, {75, 160}, {33, 205}, {41,
197}, {34, 206}, {68, 168}, {76, 160}, {102, 139}, {57, 215}, {101, 139}, {58,
212}, {59, 213}, {76, 162}, {33, 206}, {41, 198}, {34, 205}, {58, 213}, {59,
212}, {35, 211}, {103, 151}, {34, 211}, {102, 151}, {49, 192}, {69, 180}, {35,
209}, {104, 154}, {36, 214}, {35, 208}, {36, 215}, {56, 203}, {36, 208}, {104,
156}, {52, 192}, {56, 204}, {36, 209}, {77, 184}, {33, 215}, {34, 212}, {69,
179}, {70, 176}, {71, 177}, {33, 214}, {103, 144}, {35, 212}, {70, 177}, {71,
176}, {77, 186}, {79, 183}, {104, 144}, {53, 204}, {101, 156}, {78, 183}, {79,
181}, {72, 179}, {78, 181}, {45, 209}, {80, 172}, {72, 180}, {53, 203}, {103,
153}, {80, 174}, {54, 200}, {55, 201}, {45, 210}, {102, 153}, {101, 154}, {54,
201}, {55, 200} }>;
(II) A more general form is to represent the graph as the orbit of {107, 120}
under the group generated by the following permutations:
a: (1, 5, 3, 7)(2, 8, 4, 6)(10, 12)(13, 32)(14, 31)(15, 30)(16, 29)(17, 28)(18,
27)(19, 26)(20, 25)(21, 33)(22, 34)(23, 35)(24, 36)(37, 41)(38, 44)(39, 43)(40,
42)(45, 47)(49, 68, 52, 65)(50, 67, 51, 66)(53, 61, 56, 64)(54, 62, 55, 63)(57,
72)(58, 71)(59, 70)(60, 69)(73, 80)(74, 77)(75, 78)(76, 79)(82, 84)(85, 104)(86,
103)(87, 102)(88, 101)(89, 100, 92, 97)(90, 99, 91, 98)(93, 105, 96, 108)(94,
106, 95, 107)(109, 130, 112, 127)(110, 131, 113, 128)(111, 132, 114, 129)(115,
124, 118, 121)(116, 125, 119, 122)(117, 126, 120, 123)(133, 142)(134, 143)(135,
144)(136, 139)(137, 140)(138, 141)(145, 196)(146, 197)(147, 198)(148, 193)(149,
194)(150, 195)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 204)(157,
184)(158, 185)(159, 186)(160, 181)(161, 182)(162, 183)(163, 187)(164, 188)(165,
189)(166, 190)(167, 191)(168, 192)(169, 205)(170, 206)(171, 207)(172, 208)(173,
209)(174, 210)(175, 211)(176, 212)(177, 213)(178, 214)(179, 215)(180, 216) (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: (13, 14)(15, 16)(61, 62)(63, 64)(101, 102)(103, 104)(151, 154)(152, 155)(153,
156)
c: (21, 23)(22, 24)(45, 48)(46, 47)(69, 70)(71, 72)(77, 80)(78, 79)(97, 98)(99,
100)(169, 172)(170, 173)(171, 174)(175, 178)(176, 179)(177, 180)
d: (21, 22)(23, 24)(69, 70)(71, 72)(97, 98)(99, 100)(175, 178)(176, 179)(177,
180)
e: (5, 6)(7, 8)(65, 68)(66, 67)(97, 100)(98, 99)(127, 130)(128, 131)(129,
132)
f: (33, 34)(35, 36)(57, 58)(59, 60)(89, 90)(91, 92)(211, 214)(212, 215)(213,
216)
g: (2, 4)(5, 11, 7, 9)(6, 10, 8, 12)(13, 28)(14, 27)(15, 26)(16, 25)(17, 36, 20,
33)(18, 35, 19, 34)(21, 29, 24, 32)(22, 30, 23, 31)(38, 40)(41, 45, 43, 47)(42,
48, 44, 46)(49, 64)(50, 63)(51, 62)(52, 61)(53, 69, 56, 72)(54, 70, 55, 71)(57,
68, 60, 65)(58, 67, 59, 66)(73, 76, 75, 74)(77, 82, 80, 81)(78, 83, 79, 84)(85,
100, 88, 97)(86, 99, 87, 98)(89, 108)(90, 107)(91, 106)(92, 105)(93, 101, 96,
104)(94, 102, 95, 103)(109, 118)(110, 119)(111, 120)(112, 115)(113, 116)(114,
117)(121, 139, 124, 142)(122, 140, 125, 143)(123, 141, 126, 144)(127, 133, 130,
136)(128, 134, 131, 137)(129, 135, 132, 138)(145, 184)(146, 185)(147, 186)(148,
181)(149, 182)(150, 183)(151, 187)(152, 188)(153, 189)(154, 190)(155, 191)(156,
192)(157, 208, 160, 205)(158, 209, 161, 206)(159, 210, 162, 207)(163, 211)(164,
212)(165, 213)(166, 214)(167, 215)(168, 216)(169, 193, 172, 196)(170, 194, 173,
197)(171, 195, 174, 198)(175, 199)(176, 200)(177, 201)(178, 202)(179, 203)(180,
204)
h: (17, 18)(19, 20)(65, 66)(67, 68)(105, 106)(107, 108)(163, 166)(164, 167)(165,
168)
m: (25, 28)(26, 27)(37, 38)(39, 40)(77, 78)(79, 80)(181, 184)(182, 185)(183,
186)
n1: (2, 4)(5, 37, 9, 73)(6, 38, 10, 74)(7, 39, 11, 75)(8, 40, 12, 76)(13, 57,
17, 93)(14, 58, 18, 94)(15, 59, 19, 95)(16, 60, 20, 96)(22, 24)(25, 101, 33,
65)(26, 102, 34, 66)(27, 103, 35, 67)(28, 104, 36, 68)(29, 31)(41, 53, 81,
85)(42, 54, 82, 86)(43, 55, 83, 87)(44, 56, 84, 88)(45, 100, 77, 72)(46, 97, 78,
69)(47, 98, 79, 70)(48, 99, 80, 71)(49, 64, 89, 108)(50, 63, 90, 107)(51, 62,
91, 106)(52, 61, 92, 105)(109, 118, 110, 119)(111, 120)(112, 115, 113, 116)(114,
117)(121, 146, 134, 157)(122, 147, 133, 159)(123, 145, 135, 158)(124, 149, 137,
160)(125, 150, 136, 162)(126, 148, 138, 161)(127, 183, 140, 207)(128, 182, 139,
205)(129, 181, 141, 206)(130, 186, 143, 210)(131, 185, 142, 208)(132, 184, 144,
209)(151, 212, 164, 187)(152, 213, 163, 189)(153, 211, 165, 188)(154, 215, 167,
190)(155, 216, 166, 192)(156, 214, 168, 191)(169, 179, 170, 178)(171, 180)(172,
176, 173, 175)(174, 177)(193, 199, 194, 200)(195, 201)(196, 202, 197, 203)(198,
204)
a1: (33, 36)(34, 35)(45, 46)(47, 48)(73, 74)(75, 76)(205, 208)(206, 209)(207,
210)
b1: (13, 16)(14, 15)(25, 28)(26, 27)(37, 39)(38, 40)(77, 78)(79, 80)(81, 84)(82,
83)(145, 148)(146, 149)(147, 150)(181, 184)(182, 185)(183, 186)
c1: (5, 8)(6, 7)(29, 30)(31, 32)(53, 55)(54, 56)(85, 86)(87, 88)(93, 96)(94,
95)(121, 124)(122, 125)(123, 126)(199, 202)(200, 203)(201, 204)
d1: (29, 30)(31, 32)(53, 54)(55, 56)(85, 86)(87, 88)(199, 202)(200, 203)(201,
204)
e1: (17, 20)(18, 19)(29, 32)(30, 31)(41, 43)(42, 44)(73, 76)(74, 75)(81, 82)(83,
84)(157, 160)(158, 161)(159, 162)(193, 196)(194, 197)(195, 198)
f1: (25, 26)(27, 28)(49, 50)(51, 52)(93, 94)(95, 96)(187, 190)(188, 191)(189,
192)
g1: (9, 11)(10, 12)(57, 60)(58, 59)(69, 72)(70, 71)(85, 88)(86, 87)(101,
104)(102, 103)(133, 136)(134, 137)(135, 138)(139, 142)(140, 143)(141, 144)
h1: (29, 32)(30, 31)(41, 42)(43, 44)(81, 82)(83, 84)(193, 196)(194, 197)(195,
198)
m1: (1, 2)(3, 4)(61, 64)(62, 63)(105, 108)(106, 107)(115, 118)(116, 119)(117,
120)
n2: (9, 10)(11, 12)(69, 72)(70, 71)(101, 104)(102, 103)(139, 142)(140, 143)(141,
144)
C4[ 216, 83 ]
216
-1 110 118 119 109
-2 110 115 116 109
-3 112 113 115 116
-4 112 113 118 119
-5 121 122 130 131
-6 121 122 127 128
-7 124 125 127 128
-8 124 125 130 131
-9 143 133 134 142
-10 133 134 139 140
-11 136 137 139 140
-12 143 136 137 142
-13 154 155 145 146
-14 145 146 151 152
-15 148 149 151 152
-16 154 155 148 149
-17 166 167 157 158
-18 157 158 163 164
-19 160 161 163 164
-20 166 167 160 161
-21 178 179 169 170
-22 176 169 170 175
-23 176 172 173 175
-24 178 179 172 173
-25 190 191 181 182
-26 187 188 181 182
-27 187 188 184 185
-28 190 191 184 185
-29 202 203 193 194
-30 199 200 193 194
-31 199 200 196 197
-32 202 203 196 197
-33 214 215 205 206
-34 211 212 205 206
-35 209 211 212 208
-36 209 214 215 208
-37 146 147 185 186
-38 146 147 182 183
-39 149 182 150 183
-40 149 150 185 186
-41 198 158 159 197
-42 158 159 194 195
-43 161 194 162 195
-44 198 161 162 197
-45 209 210 170 171
-46 170 171 206 207
-47 173 206 174 207
-48 209 210 173 174
-49 110 111 191 192
-50 110 111 188 189
-51 188 189 113 114
-52 113 114 191 192
-53 122 123 203 204
-54 122 123 200 201
-55 200 201 125 126
-56 125 126 203 204
-57 134 135 215 216
-58 134 135 212 213
-59 212 213 137 138
-60 137 138 215 216
-61 155 156 116 117
-62 116 117 152 153
-63 119 152 120 153
-64 155 156 119 120
-65 167 168 128 129
-66 165 128 129 164
-67 132 165 131 164
-68 132 167 168 131
-69 179 180 140 141
-70 176 177 140 141
-71 143 176 144 177
-72 143 144 179 180
-73 210 157 159 208
-74 157 159 205 207
-75 160 205 162 207
-76 210 160 162 208
-77 169 171 184 186
-78 169 181 171 183
-79 181 172 183 174
-80 172 184 174 186
-81 198 145 147 196
-82 145 147 193 195
-83 148 193 150 195
-84 198 148 150 196
-85 133 135 202 204
-86 133 199 135 201
-87 199 201 136 138
-88 136 202 138 204
-89 111 214 216 109
-90 111 211 213 109
-91 112 211 114 213
-92 112 114 214 216
-93 121 123 190 192
-94 121 187 123 189
-95 187 189 124 126
-96 124 190 126 192
-97 178 180 127 129
-98 177 127 129 175
-99 132 177 130 175
-100 132 178 180 130
-101 154 156 139 141
-102 139 151 141 153
-103 144 151 142 153
-104 154 144 156 142
-105 166 168 115 117
-106 165 115 117 163
-107 165 118 163 120
-108 166 168 118 120
-109 1 89 2 90
-110 1 2 49 50
-111 89 90 49 50
-112 3 91 4 92
-113 3 4 51 52
-114 91 92 51 52
-115 2 3 105 106
-116 2 3 61 62
-117 61 105 62 106
-118 1 4 107 108
-119 1 4 63 64
-120 63 107 64 108
-121 5 93 6 94
-122 5 6 53 54
-123 93 94 53 54
-124 7 95 8 96
-125 55 56 7 8
-126 55 56 95 96
-127 6 7 97 98
-128 66 6 7 65
-129 66 97 65 98
-130 99 100 5 8
-131 67 68 5 8
-132 99 67 100 68
-133 85 9 86 10
-134 57 58 9 10
-135 57 58 85 86
-136 11 88 12 87
-137 11 12 59 60
-138 88 59 60 87
-139 11 101 102 10
-140 11 69 70 10
-141 101 69 102 70
-142 12 103 104 9
-143 12 71 72 9
-144 103 71 104 72
-145 13 14 81 82
-146 13 14 37 38
-147 37 81 38 82
-148 15 16 83 84
-149 15 16 39 40
-150 39 83 40 84
-151 14 102 15 103
-152 14 15 62 63
-153 102 103 62 63
-154 13 101 16 104
-155 13 16 61 64
-156 101 104 61 64
-157 17 18 73 74
-158 17 18 41 42
-159 73 41 74 42
-160 19 20 75 76
-161 44 19 20 43
-162 44 75 43 76
-163 18 106 19 107
-164 66 67 18 19
-165 66 67 106 107
-166 17 105 20 108
-167 68 17 20 65
-168 68 105 108 65
-169 22 77 78 21
-170 22 45 46 21
-171 77 45 78 46
-172 23 24 79 80
-173 23 24 47 48
-174 79 47 80 48
-175 22 99 23 98
-176 22 23 70 71
-177 99 70 71 98
-178 100 24 97 21
-179 24 69 72 21
-180 100 69 72 97
-181 78 79 25 26
-182 25 26 38 39
-183 78 79 38 39
-184 77 80 27 28
-185 37 27 28 40
-186 77 80 37 40
-187 26 27 94 95
-188 26 27 50 51
-189 50 94 51 95
-190 25 93 28 96
-191 25 49 28 52
-192 49 93 52 96
-193 82 83 29 30
-194 29 30 42 43
-195 82 83 42 43
-196 81 84 31 32
-197 44 41 31 32
-198 44 81 84 41
-199 30 31 86 87
-200 55 30 31 54
-201 55 86 54 87
-202 88 29 85 32
-203 56 29 53 32
-204 88 56 85 53
-205 33 34 74 75
-206 33 34 46 47
-207 46 47 74 75
-208 35 36 73 76
-209 45 35 36 48
-210 45 48 73 76
-211 34 35 90 91
-212 34 35 58 59
-213 90 58 91 59
-214 33 89 36 92
-215 33 57 36 60
-216 89 57 92 60
0