Graph forms
for C4 [ 216, 80 ] = BGCG(W(6,2),C_9,3)
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On this page are computer-accessible forms for the graph C4[ 216, 80 ] =
BGCG(W(6,2),C_9,3).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {8, 15}, {200, 207}, {104, 111}, {80, 87}, {32, 39}, {56, 63},
{128, 135}, {152, 159}, {176, 183}, {7, 15}, {199, 207}, {192, 200}, {113, 121},
{103, 111}, {96, 104}, {80, 88}, {17, 25}, {32, 40}, {48, 56}, {55, 63}, {65,
73}, {128, 136}, {144, 152}, {151, 159}, {161, 169}, {176, 184}, {7, 14}, {199,
206}, {192, 201}, {103, 110}, {96, 105}, {82, 91}, {34, 43}, {48, 57}, {55, 62},
{130, 139}, {144, 153}, {151, 158}, {178, 187}, {33, 43}, {81, 91}, {129, 139},
{177, 187}, {18, 25}, {116, 127}, {114, 121}, {84, 95}, {81, 90}, {20, 31}, {33,
42}, {36, 47}, {66, 73}, {68, 79}, {129, 138}, {132, 143}, {162, 169}, {164,
175}, {177, 186}, {180, 191}, {1, 13}, {194, 206}, {193, 205}, {115, 127}, {114,
126}, {98, 110}, {97, 109}, {83, 95}, {2, 14}, {18, 30}, {19, 31}, {22, 26},
{35, 47}, {49, 61}, {50, 62}, {66, 78}, {67, 79}, {70, 74}, {118, 122}, {131,
143}, {145, 157}, {146, 158}, {162, 174}, {163, 175}, {166, 170}, {179, 191},
{19, 30}, {115, 126}, {83, 94}, {22, 27}, {23, 26}, {35, 46}, {67, 78}, {70,
75}, {71, 74}, {118, 123}, {119, 122}, {131, 142}, {163, 174}, {166, 171}, {167,
170}, {179, 190}, {21, 27}, {117, 123}, {82, 92}, {34, 44}, {69, 75}, {130,
140}, {165, 171}, {178, 188}, {2, 13}, {194, 205}, {98, 109}, {50, 61}, {146,
157}, {5, 21}, {198, 214}, {197, 213}, {109, 125}, {102, 118}, {101, 117}, {78,
94}, {77, 93}, {6, 22}, {13, 29}, {37, 53}, {44, 60}, {68, 84}, {133, 149},
{140, 156}, {164, 180}, {173, 189}, {174, 190}, {1, 16}, {193, 208}, {97, 112},
{73, 88}, {169, 184}, {3, 17}, {195, 209}, {110, 124}, {99, 113}, {75, 89}, {14,
28}, {38, 52}, {40, 58}, {64, 82}, {134, 148}, {136, 154}, {160, 178}, {171,
185}, {6, 21}, {198, 213}, {111, 124}, {110, 125}, {102, 117}, {78, 93}, {14,
29}, {15, 28}, {38, 53}, {39, 52}, {40, 59}, {64, 83}, {134, 149}, {135, 148},
{136, 155}, {160, 179}, {174, 189}, {12, 24}, {204, 216}, {108, 120}, {36, 48},
{132, 144}, {4, 17}, {196, 209}, {100, 113}, {76, 89}, {41, 60}, {45, 56}, {65,
84}, {69, 80}, {137, 156}, {141, 152}, {161, 180}, {165, 176}, {172, 185}, {4,
18}, {196, 210}, {100, 114}, {76, 90}, {47, 57}, {71, 81}, {143, 153}, {167,
177}, {172, 186}, {3, 20}, {195, 212}, {99, 116}, {75, 92}, {171, 188}, {8, 16},
{200, 208}, {104, 112}, {79, 87}, {41, 49}, {72, 80}, {137, 145}, {168, 176},
{175, 183}, {10, 19}, {202, 211}, {106, 115}, {79, 86}, {72, 81}, {168, 177},
{175, 182}, {9, 19}, {201, 211}, {105, 115}, {9, 18}, {204, 215}, {201, 210},
{108, 119}, {105, 114}, {12, 23}, {42, 49}, {44, 55}, {138, 145}, {140, 151},
{11, 23}, {203, 215}, {107, 119}, {74, 86}, {39, 59}, {42, 54}, {43, 55}, {46,
50}, {73, 85}, {135, 155}, {138, 150}, {139, 151}, {142, 146}, {169, 181}, {170,
182}, {5, 24}, {203, 214}, {197, 216}, {107, 118}, {101, 120}, {11, 22}, {43,
54}, {46, 51}, {47, 50}, {139, 150}, {142, 147}, {143, 146}, {10, 20}, {202,
212}, {106, 116}, {45, 51}, {141, 147}, {37, 58}, {74, 85}, {133, 154}, {170,
181}, {15, 35}, {159, 179}, {29, 48}, {77, 96}, {13, 34}, {157, 178}, {20, 36},
{92, 108}, {85, 101}, {29, 45}, {30, 46}, {149, 165}, {150, 166}, {157, 173},
{25, 40}, {145, 160}, {16, 34}, {88, 106}, {86, 100}, {27, 41}, {147, 161},
{158, 172}, {16, 35}, {88, 107}, {87, 100}, {86, 101}, {30, 45}, {150, 165},
{158, 173}, {159, 172}, {84, 96}, {156, 168}, {17, 36}, {93, 104}, {89, 108},
{21, 32}, {28, 41}, {148, 161}, {23, 33}, {95, 105}, {28, 42}, {148, 162}, {27,
44}, {147, 164}, {24, 32}, {89, 97}, {31, 39}, {152, 160}, {24, 33}, {31, 38},
{154, 163}, {153, 163}, {90, 97}, {92, 103}, {153, 162}, {156, 167}, {25, 37},
{94, 98}, {91, 103}, {90, 102}, {87, 107}, {26, 38}, {155, 167}, {91, 102}, {95,
98}, {94, 99}, {149, 168}, {155, 166}, {93, 99}, {154, 164}, {26, 37}, {85,
106}, {63, 83}, {173, 192}, {61, 82}, {53, 69}, {54, 70}, {61, 77}, {181, 197},
{188, 204}, {49, 64}, {51, 65}, {62, 76}, {182, 196}, {184, 202}, {54, 69}, {62,
77}, {63, 76}, {182, 197}, {183, 196}, {184, 203}, {60, 72}, {180, 192}, {52,
65}, {189, 200}, {185, 204}, {52, 66}, {191, 201}, {51, 68}, {56, 64}, {185,
193}, {58, 67}, {57, 67}, {57, 66}, {60, 71}, {186, 193}, {188, 199}, {59, 71},
{190, 194}, {183, 203}, {186, 198}, {187, 199}, {53, 72}, {191, 194}, {190,
195}, {59, 70}, {187, 198}, {58, 68}, {189, 195}, {181, 202}, {11, 207}, {10,
205}, {5, 205}, {4, 206}, {4, 207}, {5, 206}, {1, 209}, {8, 216}, {9, 216}, {1,
210}, {7, 212}, {2, 214}, {6, 210}, {7, 211}, {2, 215}, {3, 214}, {6, 211}, {3,
213}, {12, 212}, {10, 208}, {11, 208}, {8, 213}, {12, 209}, {9, 215}, {111,
131}, {125, 144}, {109, 130}, {116, 132}, {125, 141}, {126, 142}, {121, 136},
{112, 130}, {123, 137}, {112, 131}, {126, 141}, {113, 132}, {117, 128}, {124,
137}, {119, 129}, {124, 138}, {123, 140}, {120, 128}, {127, 135}, {120, 129},
{127, 134}, {121, 133}, {122, 134}, {122, 133} }>;
(II) A more general form is to represent the graph as the orbit of {8, 15}
under the group generated by the following permutations:
a: (2, 12)(3, 5)(4, 10)(6, 8)(9, 11)(13, 209)(14, 212)(15, 211)(16, 210)(17,
205)(18, 208)(19, 207)(20, 206)(21, 213)(22, 216)(23, 215)(24, 214)(25, 193)(26,
204)(27, 197)(28, 202)(29, 195)(30, 200)(31, 199)(32, 198)(33, 203)(34, 196)(35,
201)(36, 194)(37, 185)(38, 188)(39, 187)(40, 186)(41, 181)(42, 184)(43, 183)(44,
182)(45, 189)(46, 192)(47, 191)(48, 190)(49, 169)(50, 180)(51, 173)(52, 178)(53,
171)(54, 176)(55, 175)(56, 174)(57, 179)(58, 172)(59, 177)(60, 170)(61, 161)(62,
164)(63, 163)(64, 162)(65, 157)(66, 160)(67, 159)(68, 158)(69, 165)(70, 168)(71,
167)(72, 166)(73, 145)(74, 156)(75, 149)(76, 154)(77, 147)(78, 152)(79, 151)(80,
150)(81, 155)(82, 148)(83, 153)(84, 146)(85, 137)(86, 140)(87, 139)(88, 138)(89,
133)(90, 136)(91, 135)(92, 134)(93, 141)(94, 144)(95, 143)(96, 142)(97, 121)(98,
132)(99, 125)(100, 130)(101, 123)(102, 128)(103, 127)(104, 126)(105, 131)(106,
124)(107, 129)(108, 122)(109, 113)(110, 116)(111, 115)(112, 114)(118, 120) (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: (3, 9)(6, 12)(17, 18)(19, 20)(21, 24)(22, 23)(27, 33)(30, 36)(41, 42)(43,
44)(45, 48)(46, 47)(51, 57)(54, 60)(65, 66)(67, 68)(69, 72)(70, 71)(75, 81)(78,
84)(89, 90)(91, 92)(93, 96)(94, 95)(99, 105)(102, 108)(113, 114)(115, 116)(117,
120)(118, 119)(123, 129)(126, 132)(137, 138)(139, 140)(141, 144)(142, 143)(147,
153)(150, 156)(161, 162)(163, 164)(165, 168)(166, 167)(171, 177)(174, 180)(185,
186)(187, 188)(189, 192)(190, 191)(195, 201)(198, 204)(209, 210)(211, 212)(213,
216)(214, 215)
c: (1, 34)(2, 29)(3, 30)(4, 31)(5, 26)(6, 27)(7, 28)(8, 35)(9, 36)(10, 25)(11,
32)(12, 33)(17, 19)(18, 20)(21, 22)(23, 24)(37, 205)(38, 206)(39, 207)(40,
208)(41, 211)(42, 212)(43, 209)(44, 210)(45, 214)(46, 213)(47, 216)(48, 215)(49,
202)(50, 197)(51, 198)(52, 199)(53, 194)(54, 195)(55, 196)(56, 203)(57, 204)(58,
193)(59, 200)(60, 201)(61, 181)(62, 182)(63, 183)(64, 184)(65, 187)(66, 188)(67,
185)(68, 186)(69, 190)(70, 189)(71, 192)(72, 191)(73, 178)(74, 173)(75, 174)(76,
175)(77, 170)(78, 171)(79, 172)(80, 179)(81, 180)(82, 169)(83, 176)(84, 177)(85,
157)(86, 158)(87, 159)(88, 160)(89, 163)(90, 164)(91, 161)(92, 162)(93, 166)(94,
165)(95, 168)(96, 167)(97, 154)(98, 149)(99, 150)(100, 151)(101, 146)(102,
147)(103, 148)(104, 155)(105, 156)(106, 145)(107, 152)(108, 153)(109, 133)(110,
134)(111, 135)(112, 136)(113, 139)(114, 140)(115, 137)(116, 138)(117, 142)(118,
141)(119, 144)(120, 143)(121, 130)(122, 125)(123, 126)(124, 127)(128, 131)(129,
132)
d: (1, 2)(3, 6, 9, 12)(4, 11)(5, 10)(7, 8)(14, 16)(17, 22, 18, 23)(19, 24, 20,
21)(25, 26)(27, 30, 33, 36)(28, 35)(29, 34)(31, 32)(38, 40)(41, 46, 42, 47)(43,
48, 44, 45)(49, 50)(51, 54, 57, 60)(52, 59)(53, 58)(55, 56)(62, 64)(65, 70, 66,
71)(67, 72, 68, 69)(73, 74)(75, 78, 81, 84)(76, 83)(77, 82)(79, 80)(86, 88)(89,
94, 90, 95)(91, 96, 92, 93)(97, 98)(99, 102, 105, 108)(100, 107)(101, 106)(103,
104)(110, 112)(113, 118, 114, 119)(115, 120, 116, 117)(121, 122)(123, 126, 129,
132)(124, 131)(125, 130)(127, 128)(134, 136)(137, 142, 138, 143)(139, 144, 140,
141)(145, 146)(147, 150, 153, 156)(148, 155)(149, 154)(151, 152)(158, 160)(161,
166, 162, 167)(163, 168, 164, 165)(169, 170)(171, 174, 177, 180)(172, 179)(173,
178)(175, 176)(182, 184)(185, 190, 186, 191)(187, 192, 188, 189)(193, 194)(195,
198, 201, 204)(196, 203)(197, 202)(199, 200)(206, 208)(209, 214, 210, 215)(211,
216, 212, 213)
e: (2, 8)(5, 11)(13, 16)(14, 15)(21, 22)(23, 24)(26, 32)(29, 35)(37, 40)(38,
39)(45, 46)(47, 48)(50, 56)(53, 59)(61, 64)(62, 63)(69, 70)(71, 72)(74, 80)(77,
83)(85, 88)(86, 87)(93, 94)(95, 96)(98, 104)(101, 107)(109, 112)(110, 111)(117,
118)(119, 120)(122, 128)(125, 131)(133, 136)(134, 135)(141, 142)(143, 144)(146,
152)(149, 155)(157, 160)(158, 159)(165, 166)(167, 168)(170, 176)(173, 179)(181,
184)(182, 183)(189, 190)(191, 192)(194, 200)(197, 203)(205, 208)(206, 207)(213,
214)(215, 216)
C4[ 216, 80 ]
216
-1 209 210 13 16
-2 13 14 214 215
-3 213 214 17 20
-4 17 18 206 207
-5 24 205 206 21
-6 22 210 211 21
-7 211 14 212 15
-8 15 213 16 216
-9 215 18 216 19
-10 205 19 20 208
-11 22 23 207 208
-12 209 23 24 212
-13 1 34 2 29
-14 2 28 7 29
-15 35 28 7 8
-16 1 34 35 8
-17 3 25 36 4
-18 25 4 30 9
-19 30 9 31 10
-20 3 36 31 10
-21 5 27 6 32
-22 11 26 27 6
-23 11 33 12 26
-24 33 12 5 32
-25 37 17 18 40
-26 22 23 37 38
-27 22 44 41 21
-28 14 15 41 42
-29 45 13 14 48
-30 45 46 18 19
-31 38 39 19 20
-32 24 39 40 21
-33 23 24 42 43
-34 44 13 16 43
-35 46 47 15 16
-36 47 48 17 20
-37 25 58 26 53
-38 26 52 31 53
-39 59 52 31 32
-40 25 58 59 32
-41 27 49 60 28
-42 33 49 28 54
-43 33 55 34 54
-44 55 34 27 60
-45 56 29 51 30
-46 35 50 51 30
-47 35 57 36 50
-48 56 57 36 29
-49 61 41 42 64
-50 46 47 61 62
-51 45 46 68 65
-52 66 38 39 65
-53 69 37 38 72
-54 69 70 42 43
-55 44 62 63 43
-56 45 48 63 64
-57 66 67 47 48
-58 67 68 37 40
-59 70 71 39 40
-60 44 71 72 41
-61 77 49 82 50
-62 55 77 50 76
-63 55 56 83 76
-64 56 49 82 83
-65 51 73 84 52
-66 78 57 73 52
-67 78 57 79 58
-68 79 58 51 84
-69 80 53 75 54
-70 59 74 75 54
-71 59 81 60 74
-72 80 81 60 53
-73 66 88 85 65
-74 70 71 85 86
-75 89 69 70 92
-76 89 90 62 63
-77 93 61 62 96
-78 66 67 93 94
-79 67 68 86 87
-80 88 69 72 87
-81 90 91 71 72
-82 91 92 61 64
-83 94 95 63 64
-84 68 95 96 65
-85 101 73 106 74
-86 100 79 101 74
-87 100 79 80 107
-88 80 73 106 107
-89 75 97 108 76
-90 102 81 97 76
-91 102 81 103 82
-92 103 82 75 108
-93 77 99 78 104
-94 99 78 83 98
-95 83 105 84 98
-96 77 104 105 84
-97 89 90 112 109
-98 110 94 95 109
-99 113 93 94 116
-100 113 114 86 87
-101 117 85 86 120
-102 90 91 117 118
-103 110 111 91 92
-104 111 112 93 96
-105 114 115 95 96
-106 88 115 116 85
-107 88 118 119 87
-108 89 92 119 120
-109 125 97 130 98
-110 124 103 125 98
-111 124 103 104 131
-112 104 97 130 131
-113 99 121 132 100
-114 121 100 126 105
-115 126 105 127 106
-116 99 132 127 106
-117 101 123 102 128
-118 122 123 102 107
-119 122 107 129 108
-120 101 128 129 108
-121 133 113 114 136
-122 133 134 118 119
-123 137 117 118 140
-124 110 111 137 138
-125 110 144 141 109
-126 114 115 141 142
-127 134 135 115 116
-128 135 136 117 120
-129 138 139 119 120
-130 112 139 140 109
-131 143 111 112 142
-132 143 144 113 116
-133 121 154 122 149
-134 122 148 127 149
-135 155 148 127 128
-136 121 154 155 128
-137 123 145 156 124
-138 145 124 150 129
-139 150 129 151 130
-140 123 156 151 130
-141 125 147 126 152
-142 146 147 126 131
-143 132 146 131 153
-144 132 125 152 153
-145 157 137 138 160
-146 143 157 158 142
-147 161 141 142 164
-148 134 135 161 162
-149 165 133 134 168
-150 165 166 138 139
-151 158 159 139 140
-152 144 159 160 141
-153 143 144 162 163
-154 133 136 163 164
-155 166 167 135 136
-156 167 168 137 140
-157 145 178 146 173
-158 146 172 151 173
-159 179 172 151 152
-160 145 178 179 152
-161 147 169 180 148
-162 169 148 174 153
-163 154 174 153 175
-164 154 147 180 175
-165 176 149 171 150
-166 155 170 171 150
-167 155 177 156 170
-168 176 177 156 149
-169 181 161 162 184
-170 166 167 181 182
-171 165 166 188 185
-172 158 159 185 186
-173 189 157 158 192
-174 189 190 162 163
-175 182 183 163 164
-176 165 168 183 184
-177 187 167 168 186
-178 187 188 157 160
-179 190 191 159 160
-180 191 192 161 164
-181 169 202 170 197
-182 170 196 175 197
-183 176 203 196 175
-184 176 169 202 203
-185 171 193 204 172
-186 198 177 193 172
-187 198 177 199 178
-188 199 178 171 204
-189 200 173 195 174
-190 179 194 195 174
-191 179 201 180 194
-192 200 201 180 173
-193 205 185 186 208
-194 190 191 205 206
-195 209 189 190 212
-196 209 210 182 183
-197 213 181 182 216
-198 187 213 214 186
-199 187 188 206 207
-200 189 192 207 208
-201 210 211 191 192
-202 211 212 181 184
-203 214 215 183 184
-204 188 215 216 185
-205 5 193 194 10
-206 199 4 5 194
-207 11 199 200 4
-208 11 200 193 10
-209 1 12 195 196
-210 1 201 6 196
-211 201 202 6 7
-212 12 202 7 195
-213 198 3 8 197
-214 198 2 3 203
-215 2 203 204 9
-216 204 8 9 197
0