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