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