Graph forms
for C4 [ 192, 143 ] = PL(CS(R_12(11,4)[12^4],1))
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On this page are computer-accessible forms for the graph C4[ 192, 143 ] =
PL(CS(R_12(11,4)[12^4],1)).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {78, 126}, {78, 127}, {77, 127}, {77, 126}, {66, 123}, {65, 123},
{65, 124}, {66, 124}, {45, 109}, {61, 125}, {62, 126}, {42, 107}, {45, 108},
{56, 121}, {41, 107}, {46, 108}, {46, 109}, {61, 126}, {62, 125}, {41, 108},
{42, 108}, {33, 105}, {50, 122}, {48, 120}, {34, 106}, {50, 123}, {49, 123},
{33, 106}, {49, 122}, {34, 105}, {38, 106}, {38, 107}, {37, 107}, {47, 97}, {55,
121}, {37, 106}, {39, 119}, {36, 117}, {48, 97}, {39, 118}, {36, 118}, {43,
120}, {32, 116}, {44, 120}, {32, 117}, {35, 118}, {35, 117}, {47, 120}, {44,
119}, {43, 119}, {40, 118}, {40, 119}, {1, 97}, {16, 112}, {2, 98}, {16, 113},
{19, 114}, {19, 113}, {1, 98}, {12, 111}, {2, 97}, {6, 98}, {27, 127}, {23,
115}, {11, 111}, {6, 99}, {26, 127}, {23, 114}, {20, 113}, {5, 99}, {20, 114},
{8, 110}, {5, 98}, {8, 111}, {7, 111}, {28, 116}, {27, 115}, {13, 101}, {4,
109}, {13, 100}, {10, 99}, {7, 110}, {4, 110}, {31, 117}, {24, 114}, {14, 100},
{9, 99}, {14, 101}, {31, 116}, {24, 115}, {3, 110}, {9, 100}, {3, 109}, {10,
100}, {27, 116}, {28, 115}, {22, 102}, {22, 103}, {25, 104}, {14, 124}, {26,
104}, {21, 103}, {15, 125}, {14, 125}, {21, 102}, {15, 124}, {17, 101}, {29,
105}, {18, 102}, {29, 104}, {30, 104}, {17, 102}, {30, 105}, {18, 101}, {2,
122}, {3, 122}, {3, 121}, {2, 121}, {11, 112}, {12, 112}, {26, 103}, {15, 113},
{25, 103}, {15, 112}, {50, 178}, {64, 192}, {4, 133}, {51, 178}, {4, 134}, {51,
177}, {32, 163}, {50, 177}, {1, 133}, {32, 164}, {13, 137}, {13, 136}, {18,
148}, {30, 152}, {19, 149}, {1, 134}, {31, 152}, {19, 148}, {18, 149}, {31,
151}, {30, 151}, {52, 189}, {44, 166}, {52, 190}, {60, 182}, {62, 180}, {63,
181}, {44, 167}, {60, 183}, {62, 181}, {63, 180}, {35, 175}, {49, 189}, {34,
175}, {41, 167}, {48, 190}, {57, 183}, {41, 166}, {49, 190}, {48, 191}, {57,
182}, {28, 140}, {58, 170}, {59, 171}, {58, 171}, {59, 170}, {25, 139}, {45,
191}, {34, 176}, {35, 176}, {45, 190}, {59, 168}, {6, 146}, {60, 168}, {61,
169}, {7, 146}, {25, 140}, {8, 157}, {7, 145}, {8, 158}, {6, 145}, {28, 139},
{5, 157}, {36, 188}, {16, 136}, {16, 137}, {26, 128}, {33, 187}, {5, 158}, {27,
128}, {46, 178}, {47, 179}, {33, 188}, {93, 192}, {47, 178}, {46, 179}, {36,
187}, {10, 170}, {96, 192}, {24, 184}, {11, 170}, {24, 185}, {11, 169}, {10,
169}, {38, 130}, {39, 131}, {54, 146}, {55, 147}, {57, 157}, {38, 131}, {39,
130}, {54, 147}, {55, 146}, {57, 156}, {40, 142}, {56, 158}, {58, 156}, {40,
143}, {55, 144}, {56, 159}, {58, 157}, {56, 144}, {37, 143}, {53, 159}, {59,
145}, {37, 142}, {53, 158}, {21, 185}, {21, 184}, {60, 145}, {17, 161}, {43,
155}, {42, 154}, {53, 133}, {17, 160}, {53, 132}, {43, 154}, {42, 155}, {52,
134}, {54, 132}, {52, 135}, {54, 133}, {20, 160}, {51, 135}, {20, 161}, {51,
134}, {63, 138}, {63, 137}, {12, 181}, {29, 164}, {12, 182}, {23, 173}, {22,
172}, {22, 173}, {23, 172}, {9, 181}, {29, 163}, {9, 182}, {76, 140}, {91, 155},
{76, 141}, {90, 155}, {68, 135}, {67, 135}, {94, 154}, {93, 153}, {79, 139},
{82, 150}, {79, 138}, {96, 165}, {82, 151}, {75, 141}, {96, 166}, {90, 156},
{81, 151}, {75, 140}, {94, 153}, {93, 154}, {91, 156}, {81, 150}, {87, 144},
{73, 129}, {88, 144}, {64, 137}, {73, 128}, {64, 138}, {74, 128}, {67, 136},
{74, 129}, {68, 136}, {69, 148}, {92, 141}, {85, 132}, {70, 148}, {92, 142},
{86, 132}, {66, 150}, {67, 150}, {91, 142}, {70, 147}, {86, 131}, {67, 149},
{91, 141}, {69, 147}, {78, 152}, {79, 153}, {85, 131}, {66, 149}, {88, 143},
{72, 159}, {78, 153}, {79, 152}, {71, 159}, {90, 130}, {89, 129}, {87, 143},
{80, 138}, {80, 139}, {90, 129}, {89, 130}, {96, 191}, {65, 161}, {75, 171},
{74, 171}, {82, 176}, {93, 191}, {88, 186}, {83, 177}, {65, 162}, {88, 187},
{82, 177}, {83, 176}, {68, 161}, {68, 162}, {74, 172}, {71, 160}, {75, 172},
{70, 174}, {72, 160}, {77, 165}, {84, 188}, {64, 169}, {71, 174}, {77, 164},
{84, 189}, {71, 173}, {94, 180}, {70, 173}, {95, 180}, {81, 189}, {95, 179},
{81, 188}, {94, 179}, {85, 187}, {85, 186}, {83, 163}, {72, 185}, {89, 168},
{73, 184}, {83, 162}, {72, 186}, {76, 184}, {92, 168}, {80, 164}, {80, 165},
{84, 162}, {84, 163}, {86, 174}, {87, 175}, {86, 175}, {95, 166}, {87, 174},
{95, 165}, {76, 183}, {92, 167}, {69, 185}, {61, 192}, {73, 183}, {89, 167},
{69, 186} }>;
(II) A more general form is to represent the graph as the orbit of {78, 126}
under the group generated by the following permutations:
a: (1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 3, 7, 11, 15, 19, 23, 27, 31,
35, 39, 43, 47)(2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 4, 8, 12, 16, 20,
24, 28, 32, 36, 40, 44, 48)(49, 55, 59, 61, 66, 70, 74, 78, 82, 86, 90, 94, 51,
53, 57, 63, 68, 72, 76, 80, 84, 88, 92, 96)(50, 54, 58, 62, 67, 71, 73, 79, 83,
85, 91, 95, 52, 56, 60, 64, 65, 69, 75, 77, 81, 87, 89, 93)(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, 145, 169, 124, 148, 172, 127, 151, 175, 130, 154, 178,
133, 157, 181, 136, 160, 184, 139, 163, 187, 142, 166, 190)(122, 146, 170, 125,
149, 173, 128, 152, 176, 131, 155, 179, 134, 158, 182, 137, 161, 185, 140, 164,
188, 143, 167, 191)(123, 147, 171, 126, 150, 174, 129, 153, 177, 132, 156, 180,
135, 159, 183, 138, 162, 186, 141, 165, 189, 144, 168, 192) (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, 4)(5, 51)(6, 52)(7, 49)(8, 50)(9, 68)(10, 67)(11, 66)(12, 65)(14, 16)(17,
63)(18, 64)(19, 61)(20, 62)(21, 80)(22, 79)(23, 78)(24, 77)(26, 28)(29, 76)(30,
75)(31, 74)(32, 73)(33, 92)(34, 91)(35, 90)(36, 89)(38, 40)(41, 88)(42, 87)(43,
86)(44, 85)(45, 55)(46, 56)(47, 53)(48, 54)(57, 83)(58, 82)(59, 81)(60, 84)(69,
96)(70, 93)(71, 94)(72, 95)(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, 121)(110,
122)(111, 123)(112, 124)(113, 125)(114, 126)(115, 127)(116, 128)(117, 129)(118,
130)(119, 131)(120, 132)(145, 189)(146, 190)(147, 191)(148, 192)(149, 169)(150,
170)(151, 171)(152, 172)(153, 173)(154, 174)(155, 175)(156, 176)(157, 177)(158,
178)(159, 179)(160, 180)(161, 181)(162, 182)(163, 183)(164, 184)(165, 185)(166,
186)(167, 187)(168, 188)
c: (1, 2)(3, 4)(13, 14)(15, 16)(25, 26)(27, 28)(37, 38)(39, 40)(49, 52)(50,
51)(53, 56)(54, 55)(61, 64)(62, 63)(65, 68)(66, 67)(73, 76)(74, 75)(77, 80)(78,
79)(85, 88)(86, 87)(89, 92)(90, 91)(121, 133)(122, 134)(123, 135)(124, 136)(125,
137)(126, 138)(127, 139)(128, 140)(129, 141)(130, 142)(131, 143)(132, 144)
d: (5, 6)(7, 8)(17, 18)(19, 20)(29, 30)(31, 32)(41, 42)(43, 44)(53, 54)(55,
56)(57, 60)(58, 59)(65, 66)(67, 68)(69, 72)(70, 71)(77, 78)(79, 80)(81, 84)(82,
83)(89, 90)(91, 92)(93, 96)(94, 95)(145, 157)(146, 158)(147, 159)(148, 160)(149,
161)(150, 162)(151, 163)(152, 164)(153, 165)(154, 166)(155, 167)(156, 168)
e: (9, 10)(11, 12)(21, 22)(23, 24)(33, 34)(35, 36)(45, 46)(47, 48)(49, 50)(51,
52)(57, 58)(59, 60)(61, 62)(63, 64)(69, 70)(71, 72)(73, 74)(75, 76)(81, 82)(83,
84)(85, 86)(87, 88)(93, 94)(95, 96)(169, 181)(170, 182)(171, 183)(172, 184)(173,
185)(174, 186)(175, 187)(176, 188)(177, 189)(178, 190)(179, 191)(180, 192)
f: (2, 4)(5, 54)(6, 53)(7, 56)(8, 55)(9, 85)(10, 86)(11, 87)(12, 88)(13, 39)(14,
38)(15, 37)(16, 40)(17, 89)(18, 90)(19, 91)(20, 92)(21, 73)(22, 74)(23, 75)(24,
76)(25, 27)(29, 77)(30, 78)(31, 79)(32, 80)(33, 62)(34, 61)(35, 64)(36, 63)(41,
65)(42, 66)(43, 67)(44, 68)(45, 50)(46, 49)(47, 52)(48, 51)(57, 69)(58, 70)(59,
71)(60, 72)(81, 94)(82, 93)(83, 96)(84, 95)(97, 134)(98, 133)(99, 132)(100,
131)(101, 130)(102, 129)(103, 128)(104, 127)(105, 126)(106, 125)(107, 124)(108,
123)(109, 122)(110, 121)(111, 144)(112, 143)(113, 142)(114, 141)(115, 140)(116,
139)(117, 138)(118, 137)(119, 136)(120, 135)(145, 159)(146, 158)(147, 157)(148,
156)(149, 155)(150, 154)(151, 153)(160, 168)(161, 167)(162, 166)(163, 165)(169,
175)(170, 174)(171, 173)(176, 192)(177, 191)(178, 190)(179, 189)(180, 188)(181,
187)(182, 186)(183, 185)
C4[ 192, 143 ]
192
-1 133 134 97 98
-2 121 122 97 98
-3 110 121 122 109
-4 110 133 134 109
-5 99 157 158 98
-6 99 145 146 98
-7 110 111 145 146
-8 110 111 157 158
-9 99 100 181 182
-10 99 100 169 170
-11 111 112 169 170
-12 111 112 181 182
-13 100 101 136 137
-14 100 101 124 125
-15 112 113 124 125
-16 112 113 136 137
-17 101 102 160 161
-18 101 102 148 149
-19 113 114 148 149
-20 113 114 160 161
-21 102 103 184 185
-22 102 103 172 173
-23 114 115 172 173
-24 114 115 184 185
-25 103 104 139 140
-26 103 104 127 128
-27 115 116 127 128
-28 115 116 139 140
-29 104 105 163 164
-30 104 105 151 152
-31 116 117 151 152
-32 116 117 163 164
-33 187 188 105 106
-34 176 105 106 175
-35 176 117 118 175
-36 187 188 117 118
-37 143 106 107 142
-38 106 107 130 131
-39 118 119 130 131
-40 143 118 119 142
-41 166 167 107 108
-42 154 155 107 108
-43 154 155 119 120
-44 166 167 119 120
-45 190 191 108 109
-46 178 179 108 109
-47 178 179 97 120
-48 190 191 97 120
-49 122 123 189 190
-50 122 177 123 178
-51 177 134 178 135
-52 134 189 135 190
-53 132 133 158 159
-54 132 133 146 147
-55 121 144 146 147
-56 121 144 158 159
-57 156 157 182 183
-58 156 157 170 171
-59 145 168 170 171
-60 145 168 182 183
-61 125 169 126 192
-62 125 180 126 181
-63 180 137 181 138
-64 169 137 192 138
-65 123 124 161 162
-66 123 124 149 150
-67 135 136 149 150
-68 135 136 161 162
-69 147 148 185 186
-70 147 148 173 174
-71 159 160 173 174
-72 159 160 185 186
-73 128 183 129 184
-74 171 128 172 129
-75 171 172 140 141
-76 183 140 184 141
-77 165 126 127 164
-78 126 127 152 153
-79 138 139 152 153
-80 165 138 139 164
-81 188 189 150 151
-82 176 177 150 151
-83 176 177 162 163
-84 188 189 162 163
-85 132 187 131 186
-86 132 174 131 175
-87 143 144 174 175
-88 143 187 144 186
-89 167 168 129 130
-90 155 156 129 130
-91 155 156 141 142
-92 167 168 141 142
-93 154 191 192 153
-94 154 179 180 153
-95 165 166 179 180
-96 165 166 191 192
-97 1 2 47 48
-98 1 2 5 6
-99 5 6 9 10
-100 13 14 9 10
-101 13 14 17 18
-102 22 17 18 21
-103 22 25 26 21
-104 25 26 29 30
-105 33 34 29 30
-106 33 34 37 38
-107 37 38 41 42
-108 45 46 41 42
-109 45 46 3 4
-110 3 4 7 8
-111 11 12 7 8
-112 11 12 15 16
-113 15 16 19 20
-114 23 24 19 20
-115 23 24 27 28
-116 27 28 31 32
-117 35 36 31 32
-118 35 36 39 40
-119 44 39 40 43
-120 44 47 48 43
-121 55 56 2 3
-122 2 3 49 50
-123 66 49 50 65
-124 66 14 15 65
-125 14 15 61 62
-126 77 78 61 62
-127 77 78 26 27
-128 26 27 73 74
-129 89 90 73 74
-130 89 90 38 39
-131 38 39 85 86
-132 85 53 86 54
-133 1 4 53 54
-134 1 4 51 52
-135 67 68 51 52
-136 67 13 68 16
-137 13 16 63 64
-138 79 80 63 64
-139 79 25 80 28
-140 25 28 75 76
-141 91 92 75 76
-142 91 37 92 40
-143 88 37 40 87
-144 55 88 56 87
-145 59 60 6 7
-146 55 6 7 54
-147 55 69 70 54
-148 69 70 18 19
-149 66 67 18 19
-150 66 67 81 82
-151 81 82 30 31
-152 78 79 30 31
-153 78 79 93 94
-154 93 94 42 43
-155 90 91 42 43
-156 57 90 58 91
-157 57 58 5 8
-158 56 5 8 53
-159 56 71 72 53
-160 71 17 72 20
-161 68 17 20 65
-162 68 83 84 65
-163 83 29 84 32
-164 77 80 29 32
-165 77 80 95 96
-166 44 95 41 96
-167 44 89 92 41
-168 89 59 92 60
-169 11 61 64 10
-170 11 58 59 10
-171 58 59 74 75
-172 22 23 74 75
-173 22 23 70 71
-174 70 71 86 87
-175 34 35 86 87
-176 34 35 82 83
-177 82 50 83 51
-178 46 47 50 51
-179 46 47 94 95
-180 94 62 95 63
-181 12 62 63 9
-182 12 57 60 9
-183 57 60 73 76
-184 24 73 21 76
-185 24 69 72 21
-186 88 69 72 85
-187 33 88 36 85
-188 33 36 81 84
-189 81 49 84 52
-190 45 48 49 52
-191 45 48 93 96
-192 93 61 96 64
0