Graph forms
for C4 [ 192, 72 ] = PL(BC_48({0,24},{1,11})
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On this page are computer-accessible forms for the graph C4[ 192, 72 ] =
PL(BC_48({0,24},{1,11}).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {116, 119}, {115, 119}, {163, 170}, {163, 169}, {115, 120}, {116,
120}, {164, 169}, {164, 170}, {105, 121}, {105, 120}, {40, 58}, {40, 59}, {108,
120}, {108, 121}, {109, 117}, {110, 118}, {109, 118}, {110, 117}, {37, 59}, {37,
58}, {139, 171}, {154, 186}, {153, 185}, {140, 172}, {79, 109}, {159, 189}, {80,
114}, {81, 115}, {28, 63}, {158, 189}, {154, 185}, {153, 186}, {78, 109}, {80,
115}, {81, 114}, {27, 63}, {139, 172}, {140, 171}, {152, 176}, {153, 176}, {157,
180}, {158, 180}, {17, 61}, {155, 183}, {154, 182}, {18, 62}, {69, 105}, {70,
106}, {154, 183}, {158, 179}, {155, 182}, {128, 174}, {157, 179}, {129, 175},
{17, 62}, {129, 174}, {128, 175}, {18, 61}, {69, 106}, {70, 105}, {93, 108},
{150, 167}, {14, 60}, {149, 167}, {15, 61}, {94, 108}, {14, 61}, {15, 60}, {81,
101}, {153, 173}, {134, 178}, {133, 177}, {82, 102}, {94, 107}, {152, 173}, {93,
107}, {131, 181}, {81, 102}, {134, 177}, {133, 178}, {130, 181}, {82, 101},
{134, 190}, {135, 191}, {130, 187}, {135, 190}, {134, 191}, {129, 187}, {130,
184}, {131, 184}, {129, 188}, {149, 168}, {78, 112}, {150, 168}, {130, 188},
{79, 112}, {31, 95}, {32, 96}, {8, 73}, {25, 88}, {20, 85}, {8, 74}, {26, 88},
{20, 86}, {16, 84}, {16, 85}, {19, 86}, {19, 85}, {9, 65}, {57, 113}, {9, 64},
{56, 113}, {2, 72}, {3, 73}, {2, 73}, {3, 72}, {12, 64}, {56, 116}, {7, 74},
{26, 87}, {12, 65}, {57, 116}, {7, 73}, {25, 87}, {50, 98}, {51, 99}, {40, 121},
{50, 99}, {51, 98}, {57, 104}, {10, 88}, {40, 122}, {11, 89}, {58, 104}, {10,
89}, {24, 75}, {11, 88}, {24, 76}, {29, 72}, {30, 72}, {13, 85}, {54, 110}, {55,
111}, {13, 84}, {30, 71}, {54, 111}, {55, 110}, {29, 71}, {47, 117}, {32, 122},
{23, 76}, {46, 117}, {32, 123}, {27, 64}, {23, 75}, {43, 119}, {42, 118}, {28,
64}, {39, 122}, {43, 118}, {42, 119}, {58, 103}, {39, 121}, {158, 192}, {57,
103}, {159, 192}, {1, 97}, {36, 68}, {1, 96}, {36, 69}, {4, 96}, {33, 69}, {6,
98}, {5, 97}, {4, 97}, {33, 68}, {29, 123}, {5, 98}, {29, 122}, {6, 97}, {22,
126}, {44, 68}, {43, 67}, {23, 127}, {22, 127}, {23, 126}, {47, 66}, {47, 65},
{43, 68}, {44, 67}, {13, 124}, {48, 65}, {42, 91}, {21, 100}, {14, 124}, {48,
66}, {41, 91}, {22, 100}, {12, 127}, {11, 127}, {46, 90}, {45, 89}, {39, 83},
{38, 82}, {14, 123}, {41, 92}, {39, 82}, {38, 83}, {22, 99}, {13, 123}, {42,
92}, {21, 99}, {45, 90}, {46, 89}, {6, 124}, {49, 75}, {7, 125}, {6, 125}, {49,
74}, {7, 124}, {34, 92}, {35, 93}, {52, 74}, {31, 96}, {35, 92}, {34, 93}, {32,
95}, {52, 75}, {55, 183}, {56, 184}, {60, 189}, {21, 151}, {60, 190}, {16, 147},
{21, 150}, {16, 148}, {2, 135}, {59, 190}, {1, 135}, {59, 189}, {1, 136}, {2,
136}, {46, 164}, {11, 128}, {47, 164}, {12, 128}, {31, 147}, {30, 146}, {30,
147}, {31, 146}, {24, 150}, {24, 151}, {55, 184}, {56, 183}, {5, 149}, {49,
161}, {50, 162}, {5, 148}, {9, 152}, {10, 152}, {25, 139}, {25, 138}, {49, 162},
{50, 161}, {83, 192}, {84, 192}, {28, 138}, {28, 139}, {53, 173}, {54, 174},
{62, 166}, {63, 167}, {62, 167}, {63, 166}, {18, 136}, {19, 137}, {4, 159}, {19,
136}, {18, 137}, {15, 148}, {53, 174}, {54, 173}, {3, 159}, {15, 147}, {8, 148},
{8, 149}, {10, 151}, {9, 151}, {53, 171}, {53, 170}, {35, 131}, {45, 141}, {36,
132}, {45, 140}, {44, 142}, {3, 160}, {44, 143}, {4, 160}, {41, 143}, {35, 132},
{41, 142}, {36, 131}, {17, 161}, {17, 160}, {20, 160}, {38, 146}, {37, 145},
{20, 161}, {37, 146}, {38, 145}, {26, 162}, {27, 163}, {26, 163}, {34, 155},
{27, 162}, {51, 138}, {33, 155}, {51, 137}, {48, 140}, {33, 156}, {48, 141},
{52, 137}, {34, 156}, {52, 138}, {100, 170}, {100, 171}, {125, 165}, {126, 166},
{125, 166}, {126, 165}, {76, 172}, {90, 186}, {91, 187}, {101, 133}, {77, 172},
{113, 144}, {78, 175}, {90, 187}, {91, 186}, {101, 132}, {111, 142}, {77, 175},
{114, 144}, {111, 141}, {77, 169}, {76, 169}, {80, 181}, {80, 182}, {94, 180},
{84, 191}, {95, 180}, {83, 191}, {104, 132}, {104, 133}, {95, 177}, {94, 177},
{87, 165}, {86, 165}, {70, 178}, {71, 179}, {70, 179}, {71, 178}, {79, 182},
{67, 185}, {79, 181}, {102, 156}, {103, 157}, {106, 144}, {107, 145}, {66, 185},
{102, 157}, {103, 156}, {106, 145}, {107, 144}, {77, 176}, {114, 143}, {112,
141}, {66, 188}, {113, 143}, {112, 142}, {78, 176}, {86, 168}, {67, 188}, {87,
168} }>;
(II) A more general form is to represent the graph as the orbit of {116, 119}
under the group generated by the following permutations:
a: (2, 4)(5, 18)(6, 19)(7, 20)(8, 17)(10, 12)(14, 16)(21, 28)(22, 25)(23,
26)(24, 27)(29, 192)(30, 189)(31, 190)(32, 191)(34, 36)(38, 40)(41, 184)(42,
181)(43, 182)(44, 183)(45, 174)(46, 175)(47, 176)(48, 173)(50, 52)(53, 140)(54,
141)(55, 142)(56, 143)(57, 144)(58, 145)(59, 146)(60, 147)(61, 148)(62, 149)(63,
150)(64, 151)(65, 152)(66, 153)(67, 154)(68, 155)(69, 156)(70, 157)(71, 158)(72,
159)(73, 160)(74, 161)(75, 162)(76, 163)(77, 164)(78, 117)(79, 118)(80, 119)(81,
120)(82, 121)(83, 122)(84, 123)(85, 124)(86, 125)(87, 126)(88, 127)(89, 128)(90,
129)(91, 130)(92, 131)(93, 132)(94, 133)(95, 134)(96, 135)(97, 136)(98, 137)(99,
138)(100, 139)(101, 108)(102, 105)(103, 106)(104, 107)(110, 112)(114, 116)(166,
168)(170, 172)(178, 180)(186, 188) (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: (5, 32)(6, 31)(7, 30)(8, 29)(9, 115)(10, 116)(11, 113)(12, 114)(13, 15)(14,
16)(17, 192)(18, 191)(19, 190)(20, 189)(21, 108)(22, 107)(23, 106)(24, 105)(25,
104)(26, 103)(27, 102)(28, 101)(33, 169)(34, 170)(35, 171)(36, 172)(37, 165)(38,
166)(39, 167)(40, 168)(41, 174)(42, 173)(43, 176)(44, 175)(45, 184)(46, 183)(47,
182)(48, 181)(49, 179)(50, 180)(51, 177)(52, 178)(53, 92)(54, 91)(55, 90)(56,
89)(57, 88)(58, 87)(59, 86)(60, 85)(61, 84)(62, 83)(63, 82)(64, 81)(65, 80)(66,
79)(67, 78)(68, 77)(69, 76)(70, 75)(71, 74)(72, 73)(93, 100)(94, 99)(95, 98)(96,
97)(109, 185)(110, 186)(111, 187)(112, 188)(117, 154)(118, 153)(119, 152)(120,
151)(121, 150)(122, 149)(123, 148)(124, 147)(125, 146)(126, 145)(127, 144)(128,
143)(129, 142)(130, 141)(131, 140)(132, 139)(133, 138)(134, 137)(135, 136)(155,
164)(156, 163)(157, 162)(158, 161)(159, 160)
c: (1, 2)(3, 4)(5, 8)(6, 7)(9, 10)(11, 12)(13, 14)(15, 16)(17, 20)(18, 19)(21,
24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 34)(35, 36)(37, 38)(39, 40)(41,
44)(42, 43)(45, 48)(46, 47)(49, 50)(51, 52)(53, 77)(54, 78)(55, 79)(56, 80)(57,
81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67,
91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)(73, 97)(74, 98)(75, 99)(76,
100)(101, 104)(102, 103)(105, 108)(106, 107)(109, 110)(111, 112)(113, 114)(115,
116)(165, 166)(167, 168)(169, 170)(171, 172)(173, 176)(174, 175)(177, 178)(179,
180)(181, 184)(182, 183)(185, 186)(187, 188)(189, 192)(190, 191)
d: (1, 5)(2, 8)(3, 7)(4, 6)(9, 101)(10, 104)(11, 103)(12, 102)(13, 17)(14,
20)(15, 19)(16, 18)(21, 177)(22, 180)(23, 179)(24, 178)(25, 37)(26, 40)(27,
39)(28, 38)(29, 49)(30, 52)(31, 51)(32, 50)(33, 175)(34, 174)(35, 173)(36,
176)(41, 111)(42, 110)(43, 109)(44, 112)(45, 113)(46, 116)(47, 115)(48, 114)(53,
93)(54, 92)(55, 91)(56, 90)(57, 89)(58, 88)(59, 87)(60, 86)(61, 85)(62, 84)(63,
83)(64, 82)(65, 81)(66, 80)(67, 79)(68, 78)(69, 77)(70, 76)(71, 75)(72, 74)(94,
100)(95, 99)(96, 98)(105, 169)(106, 172)(107, 171)(108, 170)(117, 119)(120,
164)(121, 163)(122, 162)(123, 161)(124, 160)(125, 159)(126, 158)(127, 157)(128,
156)(129, 155)(130, 154)(131, 153)(132, 152)(133, 151)(134, 150)(135, 149)(136,
148)(137, 147)(138, 146)(139, 145)(140, 144)(141, 143)(165, 189)(166, 192)(167,
191)(168, 190)(181, 185)(182, 188)(183, 187)(184, 186)
C4[ 192, 72 ]
192
-1 135 136 96 97
-2 135 136 72 73
-3 159 72 160 73
-4 159 160 96 97
-5 148 149 97 98
-6 124 125 97 98
-7 124 125 73 74
-8 148 149 73 74
-9 151 64 152 65
-10 88 89 151 152
-11 88 89 127 128
-12 127 128 64 65
-13 123 124 84 85
-14 123 124 60 61
-15 147 60 148 61
-16 147 148 84 85
-17 61 160 62 161
-18 136 137 61 62
-19 136 137 85 86
-20 160 161 85 86
-21 99 100 150 151
-22 99 100 126 127
-23 126 127 75 76
-24 150 151 75 76
-25 88 138 139 87
-26 88 162 163 87
-27 63 162 64 163
-28 138 139 63 64
-29 122 123 71 72
-30 146 147 71 72
-31 146 147 95 96
-32 122 123 95 96
-33 155 68 156 69
-34 155 156 92 93
-35 132 92 93 131
-36 132 68 69 131
-37 145 58 146 59
-38 145 146 82 83
-39 121 122 82 83
-40 121 122 58 59
-41 143 91 92 142
-42 91 92 118 119
-43 67 68 118 119
-44 143 67 68 142
-45 89 90 140 141
-46 89 90 117 164
-47 66 117 65 164
-48 66 140 141 65
-49 161 74 162 75
-50 99 161 162 98
-51 99 137 138 98
-52 137 138 74 75
-53 170 171 173 174
-54 110 111 173 174
-55 110 111 183 184
-56 113 116 183 184
-57 113 103 104 116
-58 37 103 104 40
-59 189 190 37 40
-60 189 14 190 15
-61 14 15 17 18
-62 166 167 17 18
-63 166 167 27 28
-64 12 27 28 9
-65 12 47 48 9
-66 188 47 48 185
-67 44 188 185 43
-68 33 44 36 43
-69 33 36 105 106
-70 178 179 105 106
-71 178 179 29 30
-72 2 3 29 30
-73 2 3 7 8
-74 49 7 8 52
-75 23 24 49 52
-76 23 24 169 172
-77 176 169 172 175
-78 176 112 109 175
-79 112 181 182 109
-80 114 115 181 182
-81 101 102 114 115
-82 101 102 38 39
-83 191 38 192 39
-84 13 191 16 192
-85 13 16 19 20
-86 165 168 19 20
-87 165 25 168 26
-88 11 25 26 10
-89 11 45 46 10
-90 187 45 46 186
-91 187 41 42 186
-92 34 35 41 42
-93 34 35 107 108
-94 177 180 107 108
-95 177 180 31 32
-96 1 4 31 32
-97 1 4 5 6
-98 5 6 50 51
-99 22 50 51 21
-100 22 170 171 21
-101 132 133 81 82
-102 156 157 81 82
-103 57 156 58 157
-104 132 133 57 58
-105 121 69 70 120
-106 144 145 69 70
-107 144 145 93 94
-108 121 93 94 120
-109 78 79 117 118
-110 55 117 118 54
-111 55 141 54 142
-112 78 79 141 142
-113 143 56 144 57
-114 143 144 80 81
-115 80 81 119 120
-116 56 57 119 120
-117 110 46 47 109
-118 110 42 43 109
-119 115 116 42 43
-120 115 105 116 108
-121 39 105 40 108
-122 39 29 40 32
-123 13 14 29 32
-124 13 14 6 7
-125 165 166 6 7
-126 22 165 23 166
-127 11 22 12 23
-128 11 12 174 175
-129 187 188 174 175
-130 187 188 181 184
-131 35 36 181 184
-132 35 101 36 104
-133 177 101 178 104
-134 177 178 190 191
-135 1 2 190 191
-136 1 2 18 19
-137 18 51 19 52
-138 25 28 51 52
-139 25 28 171 172
-140 45 48 171 172
-141 45 111 112 48
-142 44 111 112 41
-143 44 113 114 41
-144 113 114 106 107
-145 37 38 106 107
-146 37 38 30 31
-147 15 16 30 31
-148 15 5 16 8
-149 167 168 5 8
-150 24 167 168 21
-151 24 9 10 21
-152 176 173 9 10
-153 176 173 185 186
-154 182 183 185 186
-155 33 34 182 183
-156 33 34 102 103
-157 102 179 103 180
-158 189 179 180 192
-159 189 3 4 192
-160 3 4 17 20
-161 49 17 50 20
-162 26 27 49 50
-163 26 169 27 170
-164 46 47 169 170
-165 125 126 86 87
-166 125 126 62 63
-167 149 62 150 63
-168 149 150 86 87
-169 77 163 76 164
-170 100 53 163 164
-171 100 139 140 53
-172 77 139 140 76
-173 53 152 54 153
-174 128 129 53 54
-175 77 78 128 129
-176 77 78 152 153
-177 133 134 94 95
-178 133 134 70 71
-179 157 70 158 71
-180 157 158 94 95
-181 79 80 130 131
-182 154 155 79 80
-183 55 154 56 155
-184 55 56 130 131
-185 66 154 67 153
-186 154 90 91 153
-187 90 91 129 130
-188 66 67 129 130
-189 59 158 60 159
-190 134 135 59 60
-191 134 135 83 84
-192 158 159 83 84
0