Graph forms
for C4 [ 216, 86 ] = BGCG(DW(12,3),C_3,2)
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On this page are computer-accessible forms for the graph C4[ 216, 86 ] =
BGCG(DW(12,3),C_3,2).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {35, 51}, {107, 123}, {128, 145}, {68, 86}, {140, 158}, {72, 90},
{33, 53}, {105, 125}, {67, 86}, {139, 158}, {33, 54}, {168, 191}, {160, 183},
{35, 52}, {96, 119}, {105, 126}, {107, 124}, {96, 120}, {166, 190}, {164, 188},
{162, 186}, {160, 184}, {97, 121}, {103, 127}, {130, 155}, {129, 155}, {131,
153}, {97, 122}, {166, 189}, {162, 185}, {69, 88}, {132, 153}, {71, 90}, {64,
94}, {70, 88}, {164, 187}, {27, 59}, {65, 96}, {137, 168}, {135, 166}, {133,
164}, {66, 96}, {143, 173}, {139, 169}, {138, 168}, {134, 164}, {67, 97}, {71,
101}, {28, 63}, {142, 173}, {138, 169}, {66, 97}, {70, 101}, {1, 37}, {155,
191}, {153, 189}, {147, 183}, {145, 181}, {29, 57}, {26, 62}, {11, 47}, {9, 45},
{3, 39}, {73, 109}, {75, 111}, {81, 117}, {83, 119}, {3, 38}, {155, 190}, {153,
188}, {147, 182}, {11, 46}, {9, 44}, {75, 110}, {81, 116}, {83, 118}, {69, 99},
{141, 171}, {26, 61}, {140, 171}, {31, 56}, {29, 58}, {27, 60}, {68, 99}, {14,
38}, {158, 182}, {31, 55}, {25, 49}, {24, 48}, {88, 112}, {90, 114}, {92, 116},
{94, 118}, {65, 107}, {133, 175}, {14, 37}, {158, 181}, {25, 50}, {64, 107},
{90, 113}, {94, 117}, {5, 41}, {151, 187}, {149, 185}, {7, 43}, {5, 40}, {151,
186}, {149, 184}, {143, 162}, {141, 160}, {7, 42}, {80, 126}, {142, 160}, {136,
166}, {82, 124}, {84, 122}, {72, 103}, {80, 127}, {82, 125}, {84, 123}, {92,
115}, {13, 61}, {130, 178}, {15, 63}, {1, 48}, {131, 178}, {15, 62}, {73, 120},
{144, 162}, {2, 49}, {74, 121}, {128, 180}, {132, 176}, {129, 180}, {135, 177},
{16, 39}, {134, 177}, {24, 47}, {88, 111}, {16, 40}, {22, 46}, {20, 44}, {18,
42}, {86, 110}, {137, 179}, {18, 41}, {136, 179}, {22, 45}, {86, 109}, {77,
113}, {79, 115}, {77, 112}, {79, 114}, {2, 60}, {12, 50}, {10, 52}, {8, 54}, {6,
56}, {4, 58}, {4, 59}, {144, 175}, {20, 43}, {12, 51}, {10, 53}, {8, 55}, {6,
57}, {13, 72}, {157, 216}, {17, 65}, {159, 207}, {157, 205}, {52, 100}, {23,
71}, {21, 69}, {19, 67}, {58, 106}, {17, 64}, {159, 206}, {145, 192}, {53, 100},
{23, 70}, {21, 68}, {19, 66}, {59, 106}, {146, 193}, {50, 102}, {56, 108}, {54,
98}, {60, 104}, {51, 102}, {55, 98}, {57, 108}, {63, 105}, {62, 105}, {49, 104},
{61, 103}, {28, 64}, {30, 66}, {146, 204}, {156, 194}, {154, 196}, {152, 198},
{150, 200}, {148, 202}, {30, 65}, {156, 195}, {154, 197}, {152, 199}, {150,
201}, {148, 203}, {171, 203}, {43, 74}, {47, 78}, {45, 76}, {61, 92}, {63, 94},
{46, 76}, {62, 92}, {32, 67}, {180, 215}, {176, 211}, {172, 207}, {36, 71}, {32,
68}, {178, 214}, {176, 212}, {173, 201}, {170, 206}, {34, 70}, {44, 74}, {34,
69}, {178, 213}, {175, 200}, {173, 202}, {171, 204}, {170, 205}, {168, 192},
{175, 199}, {169, 193}, {58, 83}, {57, 83}, {59, 81}, {48, 91}, {169, 194}, {36,
72}, {180, 216}, {60, 81}, {161, 209}, {179, 195}, {167, 215}, {165, 213}, {163,
211}, {56, 73}, {167, 214}, {165, 212}, {163, 210}, {161, 208}, {177, 197}, {37,
80}, {39, 82}, {38, 80}, {47, 89}, {41, 95}, {40, 95}, {179, 196}, {177, 198},
{46, 89}, {52, 77}, {39, 93}, {45, 87}, {40, 82}, {38, 93}, {44, 87}, {172,
208}, {174, 210}, {41, 84}, {54, 75}, {50, 79}, {37, 91}, {55, 73}, {53, 75},
{51, 77}, {49, 79}, {48, 78}, {43, 85}, {42, 84}, {42, 85}, {174, 209}, {21,
183}, {21, 182}, {19, 181}, {17, 191}, {23, 185}, {17, 190}, {23, 184}, {10,
184}, {15, 189}, {15, 188}, {12, 185}, {12, 186}, {13, 187}, {13, 186}, {2,
187}, {6, 191}, {4, 189}, {4, 190}, {8, 181}, {10, 183}, {2, 188}, {8, 182}, {5,
196}, {11, 202}, {9, 203}, {11, 201}, {3, 198}, {18, 215}, {16, 213}, {9, 204},
{7, 194}, {85, 144}, {1, 199}, {22, 208}, {16, 214}, {7, 193}, {6, 192}, {5,
195}, {3, 197}, {31, 216}, {1, 200}, {121, 176}, {24, 209}, {18, 216}, {111,
165}, {29, 215}, {25, 211}, {24, 210}, {25, 210}, {110, 165}, {29, 214}, {27,
213}, {109, 163}, {74, 132}, {76, 130}, {78, 128}, {27, 212}, {76, 131}, {78,
129}, {85, 133}, {124, 172}, {87, 135}, {89, 137}, {91, 139}, {93, 141}, {95,
143}, {87, 134}, {125, 172}, {89, 136}, {91, 138}, {93, 140}, {95, 142}, {31,
205}, {19, 192}, {122, 174}, {126, 170}, {123, 174}, {127, 170}, {113, 167},
{119, 161}, {112, 167}, {118, 161}, {28, 196}, {20, 205}, {28, 197}, {22, 207},
{14, 212}, {20, 206}, {120, 163}, {26, 198}, {30, 194}, {14, 211}, {30, 195},
{26, 199}, {99, 131}, {32, 193}, {119, 150}, {117, 148}, {115, 146}, {118, 148},
{100, 135}, {104, 139}, {108, 143}, {98, 134}, {101, 129}, {104, 140}, {106,
142}, {116, 146}, {98, 133}, {99, 132}, {101, 130}, {103, 128}, {106, 141}, {34,
202}, {34, 203}, {124, 149}, {112, 154}, {117, 159}, {116, 159}, {32, 204}, {36,
200}, {100, 136}, {102, 138}, {36, 201}, {126, 147}, {122, 151}, {113, 156},
{33, 207}, {127, 145}, {125, 147}, {123, 149}, {121, 151}, {120, 150}, {115,
157}, {114, 156}, {33, 206}, {114, 157}, {102, 137}, {35, 209}, {35, 208}, {109,
152}, {111, 154}, {110, 152}, {108, 144} }>;
(II) A more general form is to represent the graph as the orbit of {35, 51}
under the group generated by the following permutations:
a: (2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(14, 24)(15, 23)(16, 22)(17, 21)(18, 20)(26,
36)(27, 35)(28, 34)(29, 33)(30, 32)(37, 48)(38, 47)(39, 46)(40, 45)(41, 44)(42,
43)(49, 50)(51, 60)(52, 59)(53, 58)(54, 57)(55, 56)(61, 72)(62, 71)(63, 70)(64,
69)(65, 68)(66, 67)(74, 84)(75, 83)(76, 82)(77, 81)(78, 80)(86, 96)(87, 95)(88,
94)(89, 93)(90, 92)(98, 108)(99, 107)(100, 106)(101, 105)(102, 104)(109,
120)(110, 119)(111, 118)(112, 117)(113, 116)(114, 115)(121, 122)(123, 132)(124,
131)(125, 130)(126, 129)(127, 128)(133, 144)(134, 143)(135, 142)(136, 141)(137,
140)(138, 139)(146, 156)(147, 155)(148, 154)(149, 153)(150, 152)(158, 168)(159,
167)(160, 166)(161, 165)(162, 164)(170, 180)(171, 179)(172, 178)(173, 177)(174,
176)(181, 192)(182, 191)(183, 190)(184, 189)(185, 188)(186, 187)(193, 194)(195,
204)(196, 203)(197, 202)(198, 201)(199, 200)(205, 216)(206, 215)(207, 214)(208,
213)(209, 212)(210, 211) (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, 8)(4, 10)(6, 12)(13, 145)(14, 152)(15, 147)(16, 154)(17, 149)(18,
156)(19, 151)(20, 146)(21, 153)(22, 148)(23, 155)(24, 150)(25, 73)(26, 80)(27,
75)(28, 82)(29, 77)(30, 84)(31, 79)(32, 74)(33, 81)(34, 76)(35, 83)(36, 78)(37,
199)(38, 198)(39, 197)(40, 196)(41, 195)(42, 194)(43, 193)(44, 204)(45, 203)(46,
202)(47, 201)(48, 200)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61,
127)(62, 126)(63, 125)(64, 124)(65, 123)(66, 122)(67, 121)(68, 132)(69, 131)(70,
130)(71, 129)(72, 128)(85, 169)(86, 176)(87, 171)(88, 178)(89, 173)(90, 180)(91,
175)(92, 170)(93, 177)(94, 172)(95, 179)(96, 174)(98, 104)(100, 106)(102,
108)(109, 211)(110, 212)(111, 213)(112, 214)(113, 215)(114, 216)(115, 205)(116,
206)(117, 207)(118, 208)(119, 209)(120, 210)(133, 139)(134, 140)(135, 141)(136,
142)(137, 143)(138, 144)(158, 164)(160, 166)(162, 168)(181, 187)(182, 188)(183,
189)(184, 190)(185, 191)(186, 192)
c: (2, 8)(4, 10)(6, 12)(13, 73)(14, 80)(15, 75)(16, 82)(17, 77)(18, 84)(19,
79)(20, 74)(21, 81)(22, 76)(23, 83)(24, 78)(25, 145)(26, 152)(27, 147)(28,
154)(29, 149)(30, 156)(31, 151)(32, 146)(33, 153)(34, 148)(35, 155)(36, 150)(49,
181)(50, 192)(51, 191)(52, 190)(53, 189)(54, 188)(55, 187)(56, 186)(57, 185)(58,
184)(59, 183)(60, 182)(61, 109)(62, 110)(63, 111)(64, 112)(65, 113)(66, 114)(67,
115)(68, 116)(69, 117)(70, 118)(71, 119)(72, 120)(86, 92)(88, 94)(90, 96)(97,
157)(98, 164)(99, 159)(100, 166)(101, 161)(102, 168)(103, 163)(104, 158)(105,
165)(106, 160)(107, 167)(108, 162)(121, 205)(122, 216)(123, 215)(124, 214)(125,
213)(126, 212)(127, 211)(128, 210)(129, 209)(130, 208)(131, 207)(132, 206)(170,
176)(172, 178)(174, 180)
d: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)(13, 26, 15, 28, 17, 30, 19, 32, 21,
34, 23, 36)(14, 27, 16, 29, 18, 31, 20, 33, 22, 35, 24, 25)(37, 60, 39, 58, 41,
56, 43, 54, 45, 52, 47, 50)(38, 59, 40, 57, 42, 55, 44, 53, 46, 51, 48, 49)(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, 98, 87, 100, 89, 102, 91, 104, 93, 106, 95, 108)(86, 99, 88,
101, 90, 103, 92, 105, 94, 107, 96, 97)(109, 132, 111, 130, 113, 128, 115, 126,
117, 124, 119, 122)(110, 131, 112, 129, 114, 127, 116, 125, 118, 123, 120,
121)(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, 170, 159, 172, 161, 174, 163,
176, 165, 178, 167, 180)(158, 171, 160, 173, 162, 175, 164, 177, 166, 179, 168,
169)(181, 204, 183, 202, 185, 200, 187, 198, 189, 196, 191, 194)(182, 203, 184,
201, 186, 199, 188, 197, 190, 195, 192, 193)(205, 206, 207, 208, 209, 210, 211,
212, 213, 214, 215, 216)
e: (1, 13, 25)(2, 14, 26)(3, 15, 27)(4, 16, 28)(5, 17, 29)(6, 18, 30)(7, 19,
31)(8, 20, 32)(9, 21, 33)(10, 22, 34)(11, 23, 35)(12, 24, 36)(37, 61, 49)(38,
62, 60)(39, 63, 59)(40, 64, 58)(41, 65, 57)(42, 66, 56)(43, 67, 55)(44, 68,
54)(45, 69, 53)(46, 70, 52)(47, 71, 51)(48, 72, 50)(73, 85, 97)(74, 86, 98)(75,
87, 99)(76, 88, 100)(77, 89, 101)(78, 90, 102)(79, 91, 103)(80, 92, 104)(81, 93,
105)(82, 94, 106)(83, 95, 107)(84, 96, 108)(109, 133, 121)(110, 134, 132)(111,
135, 131)(112, 136, 130)(113, 137, 129)(114, 138, 128)(115, 139, 127)(116, 140,
126)(117, 141, 125)(118, 142, 124)(119, 143, 123)(120, 144, 122)(145, 157,
169)(146, 158, 170)(147, 159, 171)(148, 160, 172)(149, 161, 173)(150, 162,
174)(151, 163, 175)(152, 164, 176)(153, 165, 177)(154, 166, 178)(155, 167,
179)(156, 168, 180)(181, 205, 193)(182, 206, 204)(183, 207, 203)(184, 208,
202)(185, 209, 201)(186, 210, 200)(187, 211, 199)(188, 212, 198)(189, 213,
197)(190, 214, 196)(191, 215, 195)(192, 216, 194)
C4[ 216, 86 ]
216
-1 199 200 37 48
-2 187 188 49 60
-3 198 38 39 197
-4 189 58 190 59
-5 40 41 195 196
-6 56 57 191 192
-7 193 194 42 43
-8 55 181 182 54
-9 44 45 203 204
-10 183 52 184 53
-11 46 47 201 202
-12 50 51 185 186
-13 187 61 72 186
-14 211 212 37 38
-15 188 189 62 63
-16 213 214 39 40
-17 190 191 64 65
-18 215 216 41 42
-19 66 67 181 192
-20 44 205 206 43
-21 68 69 182 183
-22 45 46 207 208
-23 70 71 184 185
-24 209 210 47 48
-25 210 211 49 50
-26 198 199 61 62
-27 212 59 213 60
-28 63 64 196 197
-29 57 58 214 215
-30 66 194 195 65
-31 55 56 205 216
-32 67 68 193 204
-33 206 53 207 54
-34 69 70 202 203
-35 209 51 52 208
-36 200 201 71 72
-37 1 14 80 91
-38 3 14 80 93
-39 3 16 82 93
-40 5 16 82 95
-41 5 18 84 95
-42 7 18 84 85
-43 7 74 85 20
-44 74 9 20 87
-45 22 9 76 87
-46 11 22 89 76
-47 11 78 89 24
-48 1 78 24 91
-49 2 79 25 104
-50 12 79 25 102
-51 77 12 35 102
-52 77 100 35 10
-53 33 100 75 10
-54 33 8 75 98
-55 73 8 31 98
-56 6 73 31 108
-57 6 83 29 108
-58 4 83 29 106
-59 4 81 27 106
-60 2 81 27 104
-61 13 26 92 103
-62 15 26 92 105
-63 15 28 94 105
-64 17 28 94 107
-65 17 30 96 107
-66 19 30 96 97
-67 19 86 97 32
-68 99 86 21 32
-69 88 99 34 21
-70 88 23 34 101
-71 23 90 101 36
-72 13 90 36 103
-73 55 56 109 120
-74 44 121 132 43
-75 110 111 53 54
-76 45 46 130 131
-77 112 113 51 52
-78 47 48 128 129
-79 114 49 115 50
-80 37 38 126 127
-81 59 60 116 117
-82 124 125 39 40
-83 57 58 118 119
-84 122 123 41 42
-85 133 144 42 43
-86 110 67 68 109
-87 44 45 134 135
-88 111 112 69 70
-89 46 47 136 137
-90 113 114 71 72
-91 37 48 138 139
-92 115 61 116 62
-93 38 39 140 141
-94 117 63 118 64
-95 143 40 41 142
-96 66 119 65 120
-97 66 121 67 122
-98 55 133 134 54
-99 132 68 69 131
-100 135 136 52 53
-101 70 71 129 130
-102 137 50 138 51
-103 61 72 127 128
-104 49 60 139 140
-105 125 126 62 63
-106 58 59 141 142
-107 123 124 64 65
-108 143 56 144 57
-109 73 86 152 163
-110 165 75 86 152
-111 88 154 165 75
-112 77 88 154 167
-113 77 90 156 167
-114 79 90 156 157
-115 79 146 157 92
-116 146 81 92 159
-117 81 148 159 94
-118 148 83 94 161
-119 83 150 161 96
-120 73 150 96 163
-121 176 74 151 97
-122 84 151 97 174
-123 149 84 107 174
-124 82 149 172 107
-125 147 82 105 172
-126 80 147 170 105
-127 145 80 103 170
-128 78 145 103 180
-129 78 155 101 180
-130 155 101 178 76
-131 99 178 76 153
-132 99 176 74 153
-133 85 98 164 175
-134 177 87 98 164
-135 100 166 177 87
-136 89 100 166 179
-137 89 102 168 179
-138 91 102 168 169
-139 91 158 169 104
-140 158 93 104 171
-141 93 160 171 106
-142 160 95 106 173
-143 95 162 173 108
-144 85 162 108 175
-145 181 192 127 128
-146 115 116 193 204
-147 125 126 182 183
-148 202 203 117 118
-149 123 124 184 185
-150 200 201 119 120
-151 121 187 122 186
-152 110 198 199 109
-153 132 188 189 131
-154 111 112 196 197
-155 190 191 129 130
-156 113 114 194 195
-157 114 115 205 216
-158 181 182 139 140
-159 116 117 206 207
-160 183 184 141 142
-161 209 118 119 208
-162 143 144 185 186
-163 210 211 109 120
-164 187 133 188 134
-165 110 111 212 213
-166 189 135 190 136
-167 112 113 214 215
-168 191 137 192 138
-169 138 193 139 194
-170 126 127 205 206
-171 203 204 140 141
-172 124 125 207 208
-173 143 201 202 142
-174 209 122 210 123
-175 133 144 199 200
-176 121 132 211 212
-177 198 134 135 197
-178 213 214 130 131
-179 136 137 195 196
-180 215 128 216 129
-181 145 158 8 19
-182 147 158 8 21
-183 147 160 10 21
-184 23 149 160 10
-185 12 23 149 162
-186 12 13 151 162
-187 2 13 151 164
-188 2 15 153 164
-189 166 4 15 153
-190 155 166 4 17
-191 155 168 6 17
-192 145 168 6 19
-193 146 169 7 32
-194 156 169 7 30
-195 156 179 5 30
-196 154 179 5 28
-197 154 177 3 28
-198 177 3 26 152
-199 1 26 152 175
-200 1 36 150 175
-201 11 36 150 173
-202 11 34 148 173
-203 34 148 171 9
-204 146 171 9 32
-205 157 170 20 31
-206 33 159 170 20
-207 22 33 159 172
-208 22 35 161 172
-209 24 35 161 174
-210 24 25 163 174
-211 176 14 25 163
-212 165 176 14 27
-213 165 178 16 27
-214 167 178 16 29
-215 167 180 18 29
-216 157 180 18 31
0