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