Graph forms
for C4 [ 216, 89 ] =
BGCG(AMC(6,3,[0.1:2.2]);K2;{8,9})
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On this page are computer-accessible forms for the graph C4[ 216, 89 ] =
BGCG(AMC(6,3,[0.1:2.2]);K2;{8,9}).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {104, 110}, {106, 122}, {105, 123}, {98, 113}, {101, 118}, {100,
119}, {104, 114}, {102, 125}, {96, 126}, {99, 124}, {92, 125}, {95, 123}, {74,
111}, {94, 120}, {83, 116}, {86, 113}, {68, 109}, {82, 120}, {93, 119}, {84,
126}, {87, 124}, {94, 114}, {80, 127}, {65, 115}, {65, 117}, {69, 112}, {87,
111}, {70, 127}, {73, 115}, {79, 116}, {77, 112}, {70, 121}, {56, 122}, {50,
113}, {60, 118}, {52, 121}, {48, 126}, {55, 121}, {59, 117}, {51, 124}, {33,
112}, {63, 110}, {32, 114}, {62, 109}, {41, 124}, {45, 123}, {46, 120}, {42,
125}, {38, 126}, {40, 113}, {33, 123}, {47, 117}, {34, 127}, {44, 114}, {39,
120}, {50, 109}, {40, 119}, {14, 110}, {15, 111}, {30, 125}, {9, 109}, {20,
112}, {8, 110}, {19, 116}, {16, 122}, {25, 115}, {20, 127}, {28, 119}, {29,
115}, {5, 118}, {6, 117}, {23, 111}, {1, 122}, {2, 121}, {11, 118}, {11, 116},
{7, 135}, {8, 136}, {73, 201}, {37, 164}, {46, 175}, {71, 198}, {55, 181}, {90,
216}, {61, 191}, {74, 200}, {2, 134}, {54, 178}, {49, 181}, {31, 155}, {30,
154}, {28, 152}, {10, 142}, {39, 162}, {63, 186}, {69, 192}, {3, 133}, {35,
165}, {4, 130}, {55, 177}, {76, 202}, {6, 129}, {45, 170}, {62, 185}, {80, 215},
{24, 144}, {95, 214}, {13, 135}, {48, 186}, {41, 163}, {19, 153}, {66, 200},
{57, 178}, {90, 209}, {88, 211}, {59, 176}, {69, 206}, {22, 154}, {37, 169},
{12, 129}, {94, 211}, {47, 162}, {44, 161}, {68, 202}, {33, 174}, {89, 214},
{35, 172}, {57, 182}, {68, 203}, {16, 128}, {31, 143}, {83, 195}, {28, 141}, {7,
149}, {49, 163}, {24, 139}, {52, 167}, {84, 199}, {60, 168}, {12, 153}, {58,
175}, {77, 216}, {27, 141}, {87, 193}, {17, 134}, {27, 140}, {80, 199}, {7,
159}, {32, 184}, {72, 208}, {73, 209}, {48, 169}, {21, 143}, {26, 128}, {72,
210}, {21, 142}, {16, 140}, {95, 195}, {94, 194}, {93, 193}, {13, 144}, {58,
167}, {61, 160}, {79, 210}, {9, 150}, {91, 196}, {86, 201}, {10, 149}, {72,
215}, {29, 189}, {6, 167}, {101, 196}, {53, 148}, {34, 131}, {62, 159}, {15,
173}, {18, 177}, {108, 207}, {50, 145}, {27, 184}, {23, 180}, {104, 204}, {105,
205}, {24, 189}, {44, 137}, {37, 131}, {28, 187}, {8, 160}, {20, 188}, {26,
179}, {45, 132}, {34, 139}, {5, 175}, {63, 149}, {11, 160}, {105, 194}, {54,
157}, {21, 190}, {61, 150}, {4, 168}, {31, 179}, {23, 187}, {39, 138}, {49,
156}, {36, 138}, {107, 197}, {24, 183}, {9, 185}, {53, 133}, {52, 132}, {47,
159}, {43, 155}, {35, 147}, {21, 165}, {15, 191}, {38, 151}, {3, 177}, {48,
130}, {32, 146}, {25, 171}, {8, 186}, {1, 178}, {43, 152}, {4, 176}, {42, 158},
{38, 146}, {30, 170}, {11, 190}, {38, 147}, {12, 185}, {61, 136}, {3, 181}, {99,
213}, {98, 212}, {43, 157}, {42, 156}, {10, 188}, {9, 191}, {1, 182}, {25, 174},
{17, 166}, {16, 168}, {46, 150}, {13, 180}, {49, 136}, {46, 151}, {14, 183},
{62, 135}, {10, 176}, {36, 158}, {22, 172}, {17, 171}, {13, 182}, {42, 145},
{31, 164}, {22, 173}, {58, 129}, {29, 161}, {27, 166}, {56, 133}, {60, 130},
{107, 213}, {106, 212}, {43, 148}, {54, 137}, {57, 134}, {5, 197}, {98, 162},
{23, 215}, {66, 130}, {19, 210}, {78, 143}, {4, 198}, {106, 168}, {26, 216},
{15, 205}, {14, 204}, {71, 133}, {78, 140}, {18, 209}, {103, 164}, {92, 152},
{101, 161}, {82, 151}, {101, 160}, {85, 144}, {75, 141}, {7, 192}, {90, 157},
{86, 145}, {14, 201}, {25, 209}, {92, 148}, {6, 207}, {85, 156}, {1, 203}, {99,
169}, {18, 216}, {74, 128}, {12, 199}, {67, 136}, {2, 206}, {102, 170}, {67,
143}, {64, 141}, {92, 145}, {89, 148}, {70, 139}, {84, 153}, {2, 204}, {3, 205},
{103, 182}, {26, 200}, {20, 199}, {90, 137}, {73, 154}, {17, 197}, {100, 176},
{93, 137}, {88, 140}, {5, 208}, {76, 153}, {30, 200}, {105, 191}, {64, 150},
{66, 154}, {88, 128}, {19, 202}, {29, 196}, {81, 139}, {75, 144}, {82, 142},
{88, 132}, {18, 207}, {108, 177}, {65, 159}, {22, 201}, {102, 185}, {91, 132},
{81, 142}, {99, 131}, {103, 135}, {70, 167}, {86, 183}, {85, 180}, {71, 165},
{76, 174}, {79, 173}, {33, 194}, {53, 214}, {79, 172}, {80, 180}, {39, 194},
{37, 195}, {108, 138}, {54, 208}, {81, 183}, {52, 211}, {102, 129}, {76, 171},
{98, 138}, {40, 193}, {106, 131}, {32, 202}, {69, 174}, {71, 172}, {47, 195},
{60, 208}, {41, 196}, {107, 134}, {75, 166}, {83, 190}, {82, 188}, {64, 175},
{67, 179}, {78, 190}, {74, 187}, {100, 149}, {91, 170}, {77, 188}, {83, 162},
{51, 193}, {108, 158}, {97, 147}, {96, 146}, {89, 171}, {36, 215}, {53, 198},
{51, 192}, {56, 203}, {59, 207}, {81, 165}, {56, 205}, {34, 212}, {97, 151},
{85, 163}, {36, 210}, {35, 213}, {67, 181}, {75, 189}, {78, 184}, {57, 206},
{66, 186}, {107, 147}, {91, 163}, {50, 203}, {72, 178}, {104, 146}, {87, 173},
{45, 214}, {96, 155}, {95, 164}, {55, 204}, {64, 187}, {40, 212}, {103, 155},
{100, 152}, {93, 161}, {41, 213}, {65, 189}, {68, 184}, {51, 206}, {97, 156},
{96, 157}, {59, 198}, {84, 169}, {77, 179}, {44, 211}, {97, 158}, {89, 166},
{58, 197}, {63, 192} }>;
(II) A more general form is to represent the graph as the orbit of {104, 110}
under the group generated by the following permutations:
a: (2, 3)(4, 5)(7, 9)(10, 46)(11, 48)(12, 47)(13, 50)(14, 49)(15, 51)(16,
54)(17, 53)(18, 52)(19, 37)(20, 39)(21, 38)(22, 41)(23, 40)(24, 42)(25, 45)(26,
44)(27, 43)(29, 30)(31, 32)(34, 36)(56, 57)(58, 59)(61, 63)(64, 100)(65,
102)(66, 101)(67, 104)(68, 103)(69, 105)(70, 108)(71, 107)(72, 106)(73, 91)(74,
93)(75, 92)(76, 95)(77, 94)(78, 96)(79, 99)(80, 98)(81, 97)(83, 84)(85, 86)(88,
90)(109, 135)(110, 136)(111, 193)(112, 194)(113, 180)(114, 179)(115, 170)(116,
169)(117, 129)(118, 130)(119, 187)(120, 188)(121, 177)(122, 178)(123, 174)(124,
173)(125, 189)(126, 190)(127, 138)(128, 137)(131, 210)(132, 209)(133, 134)(139,
158)(140, 157)(141, 152)(142, 151)(143, 146)(144, 145)(147, 165)(148, 166)(149,
150)(153, 195)(154, 196)(155, 184)(156, 183)(159, 185)(160, 186)(161, 200)(162,
199)(163, 201)(164, 202)(167, 207)(168, 208)(171, 214)(172, 213)(175, 176)(181,
204)(182, 203)(191, 192)(197, 198)(205, 206)(211, 216)(212, 215) (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, 10, 45, 54, 21, 30)(2, 46, 41, 36, 24, 12)(3, 28, 37, 18, 27, 48)(4, 53,
43, 31, 26, 16)(5, 35, 42, 13, 20, 52)(6, 17, 38, 49, 23, 34)(7, 33, 44, 11, 22,
50)(8, 15, 40, 47, 25, 32)(9, 51, 39, 29, 19, 14)(55, 64, 99, 108, 75, 84)(56,
100, 95, 90, 78, 66)(57, 82, 91, 72, 81, 102)(58, 107, 97, 85, 80, 70)(59, 89,
96, 67, 74, 106)(60, 71, 92, 103, 77, 88)(61, 87, 98, 65, 76, 104)(62, 69, 94,
101, 79, 86)(63, 105, 93, 83, 73, 68)(109, 192, 194, 161, 116, 201)(110, 191,
193, 162, 115, 202)(111, 212, 117, 171, 146, 136)(112, 211, 118, 172, 145,
135)(113, 159, 174, 114, 160, 173)(119, 195, 209, 184, 186, 205)(120, 196, 210,
183, 185, 206)(121, 175, 213, 158, 144, 199)(122, 176, 214, 157, 143, 200)(123,
137, 190, 154, 203, 149)(124, 138, 189, 153, 204, 150)(125, 182, 188, 132, 208,
165)(126, 181, 187, 131, 207, 166)(127, 167, 197, 147, 156, 180)(128, 168, 198,
148, 155, 179)(129, 134, 151, 163, 215, 139)(130, 133, 152, 164, 216, 140)(141,
169, 177)(142, 170, 178)
c: (1, 55)(2, 57)(3, 56)(4, 59)(5, 58)(6, 60)(7, 63)(8, 62)(9, 61)(10, 100)(11,
102)(12, 101)(13, 104)(14, 103)(15, 105)(16, 108)(17, 107)(18, 106)(19, 91)(20,
93)(21, 92)(22, 95)(23, 94)(24, 96)(25, 99)(26, 98)(27, 97)(28, 82)(29, 84)(30,
83)(31, 86)(32, 85)(33, 87)(34, 90)(35, 89)(36, 88)(37, 73)(38, 75)(39, 74)(40,
77)(41, 76)(42, 78)(43, 81)(44, 80)(45, 79)(46, 64)(47, 66)(48, 65)(49, 68)(50,
67)(51, 69)(52, 72)(53, 71)(54, 70)(109, 136)(110, 135)(111, 194)(112, 193)(113,
179)(114, 180)(115, 169)(116, 170)(117, 130)(118, 129)(119, 188)(120, 187)(121,
178)(122, 177)(123, 173)(124, 174)(125, 190)(126, 189)(127, 137)(128, 138)(131,
209)(132, 210)(139, 157)(140, 158)(141, 151)(142, 152)(143, 145)(144, 146)(147,
166)(148, 165)(153, 196)(154, 195)(155, 183)(156, 184)(159, 186)(160, 185)(161,
199)(162, 200)(163, 202)(164, 201)(167, 208)(168, 207)(171, 213)(172, 214)(181,
203)(182, 204)(211, 215)(212, 216)
d: (1, 2, 3)(4, 7, 6, 9, 5, 8)(10, 47, 12, 46, 11, 48)(13, 52, 15, 54, 14,
53)(16, 51, 18, 50, 17, 49)(19, 38, 21, 37, 20, 39)(22, 43, 24, 45, 23, 44)(25,
42, 27, 41, 26, 40)(28, 29, 30)(31, 34, 33, 36, 32, 35)(55, 56, 57)(58, 61, 60,
63, 59, 62)(64, 101, 66, 100, 65, 102)(67, 106, 69, 108, 68, 107)(70, 105, 72,
104, 71, 103)(73, 92, 75, 91, 74, 93)(76, 97, 78, 99, 77, 98)(79, 96, 81, 95,
80, 94)(82, 83, 84)(85, 88, 87, 90, 86, 89)(109, 197, 136, 168, 192, 207)(110,
198, 135, 167, 191, 208)(111, 137, 201, 148, 144, 132)(112, 138, 202, 147, 143,
131)(113, 171, 156, 140, 124, 216)(114, 172, 155, 139, 123, 215)(115, 125, 141,
196, 200, 119)(116, 126, 142, 195, 199, 120)(117, 185, 175, 160, 130, 149)(118,
186, 176, 159, 129, 150)(121, 205, 178, 204, 133, 182)(122, 206, 177, 203, 134,
181)(127, 194, 210, 146, 165, 164)(128, 193, 209, 145, 166, 163)(151, 190, 169,
188, 162, 153)(152, 189, 170, 187, 161, 154)(157, 183, 214, 180, 211, 173)(158,
184, 213, 179, 212, 174)
e: (1, 4)(2, 6)(3, 5)(8, 9)(10, 13)(11, 15)(12, 14)(17, 18)(19, 22)(20, 24)(21,
23)(26, 27)(28, 31)(29, 33)(30, 32)(35, 36)(37, 40)(38, 42)(39, 41)(44, 45)(46,
49)(47, 51)(48, 50)(53, 54)(55, 58)(56, 60)(57, 59)(62, 63)(64, 67)(65, 69)(66,
68)(71, 72)(73, 76)(74, 78)(75, 77)(80, 81)(82, 85)(83, 87)(84, 86)(89, 90)(91,
94)(92, 96)(93, 95)(98, 99)(100, 103)(101, 105)(102, 104)(107, 108)(109,
186)(110, 185)(111, 190)(112, 189)(113, 169)(114, 170)(115, 174)(116, 173)(117,
206)(118, 205)(119, 164)(120, 163)(121, 167)(122, 168)(123, 161)(124, 162)(125,
146)(126, 145)(127, 139)(128, 140)(129, 204)(130, 203)(131, 212)(132, 211)(133,
208)(134, 207)(135, 149)(136, 150)(137, 214)(138, 213)(141, 179)(142, 180)(143,
187)(144, 188)(147, 158)(148, 157)(151, 156)(152, 155)(153, 201)(154, 202)(159,
192)(160, 191)(165, 215)(166, 216)(171, 209)(172, 210)(175, 181)(176, 182)(177,
197)(178, 198)(183, 199)(184, 200)(193, 195)(194, 196)
f: (4, 9)(5, 7)(6, 8)(10, 46)(11, 47)(12, 48)(13, 54)(14, 52)(15, 53)(16,
50)(17, 51)(18, 49)(19, 37)(20, 38)(21, 39)(22, 45)(23, 43)(24, 44)(25, 41)(26,
42)(27, 40)(31, 36)(32, 34)(33, 35)(58, 63)(59, 61)(60, 62)(64, 100)(65,
101)(66, 102)(67, 108)(68, 106)(69, 107)(70, 104)(71, 105)(72, 103)(73, 91)(74,
92)(75, 93)(76, 99)(77, 97)(78, 98)(79, 95)(80, 96)(81, 94)(85, 90)(86, 88)(87,
89)(109, 168)(110, 167)(111, 148)(112, 147)(113, 140)(114, 139)(115, 196)(116,
195)(117, 160)(118, 159)(119, 141)(120, 142)(121, 204)(122, 203)(123, 172)(124,
171)(125, 200)(126, 199)(127, 146)(128, 145)(129, 186)(130, 185)(131, 202)(132,
201)(133, 205)(134, 206)(135, 208)(136, 207)(137, 144)(138, 143)(149, 175)(150,
176)(151, 188)(152, 187)(153, 169)(154, 170)(155, 215)(156, 216)(157, 180)(158,
179)(161, 189)(162, 190)(163, 209)(164, 210)(165, 194)(166, 193)(173, 214)(174,
213)(177, 181)(178, 182)(183, 211)(184, 212)(191, 198)(192, 197)
C4[ 216, 89 ]
216
-1 122 178 203 182
-2 121 134 204 206
-3 133 177 181 205
-4 176 198 168 130
-5 118 175 197 208
-6 167 117 129 207
-7 135 159 192 149
-8 110 136 160 186
-9 191 150 185 109
-10 176 188 149 142
-11 190 116 160 118
-12 199 129 185 153
-13 144 135 180 182
-14 110 201 204 183
-15 111 191 205 173
-16 122 168 128 140
-17 166 134 171 197
-18 209 177 216 207
-19 210 202 116 153
-20 188 199 112 127
-21 143 165 190 142
-22 154 201 172 173
-23 187 111 180 215
-24 144 189 139 183
-25 209 115 171 174
-26 200 179 128 216
-27 166 140 184 141
-28 187 119 141 152
-29 189 115 161 196
-30 154 200 125 170
-31 143 155 179 164
-32 146 114 202 184
-33 112 123 194 174
-34 212 127 139 131
-35 165 147 213 172
-36 210 158 138 215
-37 169 195 131 164
-38 146 147 126 151
-39 138 194 162 120
-40 113 212 193 119
-41 124 213 163 196
-42 145 156 125 158
-43 155 157 148 152
-44 211 114 137 161
-45 132 123 170 214
-46 150 151 120 175
-47 159 117 162 195
-48 169 126 130 186
-49 156 136 181 163
-50 145 113 203 109
-51 124 192 193 206
-52 121 132 167 211
-53 198 133 148 214
-54 178 157 137 208
-55 121 177 181 204
-56 122 133 203 205
-57 134 178 182 206
-58 167 129 175 197
-59 176 198 117 207
-60 168 118 130 208
-61 136 191 160 150
-62 135 159 185 109
-63 110 192 149 186
-64 187 150 141 175
-65 189 115 159 117
-66 154 200 130 186
-67 143 179 136 181
-68 202 203 184 109
-69 112 192 206 174
-70 121 167 127 139
-71 165 198 133 172
-72 210 178 215 208
-73 154 209 201 115
-74 187 111 200 128
-75 144 166 189 141
-76 202 171 174 153
-77 188 112 179 216
-78 143 190 140 184
-79 210 116 172 173
-80 199 180 127 215
-81 165 139 183 142
-82 188 151 120 142
-83 190 116 162 195
-84 199 169 126 153
-85 144 156 180 163
-86 145 113 201 183
-87 111 124 193 173
-88 132 211 128 140
-89 166 148 214 171
-90 209 157 137 216
-91 132 170 163 196
-92 145 125 148 152
-93 137 193 161 119
-94 211 114 194 120
-95 123 214 195 164
-96 155 146 157 126
-97 156 147 158 151
-98 113 212 138 162
-99 124 169 213 131
-100 176 149 119 152
-101 160 161 118 196
-102 125 170 129 185
-103 155 135 182 164
-104 110 146 114 204
-105 123 191 194 205
-106 122 168 212 131
-107 134 147 213 197
-108 177 158 138 207
-109 68 50 62 9
-110 14 104 8 63
-111 23 15 74 87
-112 33 77 69 20
-113 50 40 86 98
-114 44 104 94 32
-115 25 29 73 65
-116 11 79 83 19
-117 47 59 6 65
-118 11 101 5 60
-119 100 93 28 40
-120 46 82 39 94
-121 55 2 70 52
-122 1 56 16 106
-123 33 45 105 95
-124 99 51 41 87
-125 102 92 30 42
-126 48 38 84 96
-127 34 80 70 20
-128 88 26 16 74
-129 12 58 102 6
-130 66 4 48 60
-131 99 34 37 106
-132 88 45 91 52
-133 56 3 71 53
-134 2 57 17 107
-135 13 103 7 62
-136 67 49 61 8
-137 44 90 93 54
-138 36 39 108 98
-139 34 24 70 81
-140 88 78 16 27
-141 27 28 64 75
-142 81 82 10 21
-143 67 78 31 21
-144 13 24 85 75
-145 92 50 42 86
-146 38 104 96 32
-147 35 38 107 97
-148 89 92 53 43
-149 100 7 63 10
-150 46 61 9 64
-151 46 38 82 97
-152 100 92 28 43
-153 12 84 19 76
-154 22 66 73 30
-155 103 96 31 43
-156 49 85 42 97
-157 90 96 43 54
-158 36 42 97 108
-159 47 7 62 65
-160 11 101 61 8
-161 44 101 93 29
-162 47 39 83 98
-163 91 49 41 85
-164 37 103 95 31
-165 35 81 71 21
-166 89 27 17 75
-167 58 70 6 52
-168 4 16 60 106
-169 99 37 48 84
-170 45 91 102 30
-171 89 25 17 76
-172 22 35 79 71
-173 22 79 15 87
-174 33 25 69 76
-175 46 58 5 64
-176 100 4 59 10
-177 55 3 18 108
-178 1 57 72 54
-179 77 67 26 31
-180 23 13 80 85
-181 55 67 3 49
-182 1 13 57 103
-183 24 14 81 86
-184 78 68 27 32
-185 12 102 62 9
-186 66 48 8 63
-187 23 28 74 64
-188 77 82 20 10
-189 24 29 75 65
-190 11 78 83 21
-191 15 61 105 9
-192 69 7 51 63
-193 93 40 51 87
-194 33 39 94 105
-195 47 37 83 95
-196 101 91 29 41
-197 58 5 17 107
-198 4 59 71 53
-199 12 80 84 20
-200 66 26 30 74
-201 22 14 73 86
-202 68 19 32 76
-203 1 56 68 50
-204 55 2 14 104
-205 56 3 15 105
-206 2 57 69 51
-207 59 6 18 108
-208 5 60 72 54
-209 90 25 18 73
-210 79 36 72 19
-211 44 88 94 52
-212 34 40 106 98
-213 99 35 41 107
-214 45 89 95 53
-215 23 36 80 72
-216 77 90 26 18
0