[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 168, 32 ] = PL(BC_42({0,21},{1,8}).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {65, 69}, {64, 69}, {33, 41}, {34, 42}, {64, 72}, {65, 72}, {147, 154}, {147, 153}, {33, 42}, {34, 41}, {96, 109}, {148, 153}, {146, 159}, {96, 110}, {148, 154}, {145, 159}, {44, 60}, {134, 150}, {133, 149}, {44, 61}, {133, 150}, {139, 152}, {136, 155}, {134, 149}, {6, 18}, {140, 152}, {138, 158}, {137, 157}, {136, 156}, {41, 61}, {7, 19}, {6, 19}, {41, 60}, {40, 61}, {7, 18}, {40, 62}, {137, 158}, {138, 157}, {12, 20}, {13, 20}, {39, 62}, {39, 61}, {135, 156}, {140, 151}, {13, 17}, {139, 151}, {135, 155}, {12, 17}, {19, 51}, {20, 52}, {83, 114}, {73, 107}, {78, 108}, {83, 113}, {73, 106}, {88, 123}, {79, 108}, {65, 101}, {94, 122}, {93, 121}, {88, 124}, {66, 102}, {81, 117}, {82, 118}, {84, 113}, {79, 105}, {84, 114}, {19, 52}, {94, 121}, {93, 122}, {24, 63}, {20, 51}, {65, 102}, {66, 101}, {78, 105}, {81, 118}, {82, 117}, {23, 63}, {74, 98}, {75, 99}, {74, 99}, {89, 112}, {75, 98}, {90, 112}, {87, 124}, {2, 46}, {87, 123}, {22, 58}, {21, 57}, {3, 47}, {82, 126}, {83, 127}, {2, 47}, {3, 46}, {82, 127}, {83, 126}, {21, 58}, {22, 57}, {4, 52}, {88, 104}, {28, 44}, {27, 43}, {77, 125}, {81, 97}, {4, 53}, {145, 160}, {95, 110}, {89, 104}, {76, 125}, {80, 97}, {95, 109}, {146, 160}, {75, 120}, {1, 53}, {151, 163}, {150, 162}, {76, 120}, {80, 100}, {1, 52}, {151, 162}, {150, 163}, {90, 111}, {81, 100}, {89, 111}, {27, 44}, {28, 43}, {94, 102}, {156, 164}, {95, 103}, {77, 116}, {157, 164}, {95, 102}, {94, 103}, {78, 116}, {76, 119}, {17, 45}, {157, 161}, {89, 101}, {18, 46}, {75, 119}, {78, 115}, {156, 161}, {88, 101}, {77, 115}, {84, 106}, {17, 46}, {18, 45}, {84, 107}, {22, 86}, {23, 87}, {22, 87}, {23, 86}, {45, 111}, {50, 112}, {45, 110}, {51, 112}, {24, 92}, {24, 93}, {38, 96}, {39, 96}, {21, 93}, {49, 121}, {21, 92}, {48, 121}, {48, 124}, {54, 122}, {55, 123}, {49, 124}, {54, 123}, {55, 122}, {59, 104}, {1, 85}, {2, 86}, {60, 104}, {56, 110}, {1, 86}, {31, 72}, {23, 64}, {2, 85}, {56, 111}, {3, 91}, {31, 71}, {24, 64}, {4, 92}, {60, 103}, {25, 69}, {26, 70}, {59, 103}, {51, 109}, {3, 92}, {26, 69}, {25, 70}, {4, 91}, {50, 109}, {10, 107}, {37, 68}, {9, 107}, {38, 68}, {5, 97}, {6, 98}, {9, 108}, {38, 67}, {15, 106}, {10, 108}, {37, 67}, {15, 105}, {5, 98}, {32, 71}, {6, 97}, {11, 99}, {43, 67}, {42, 66}, {32, 72}, {12, 100}, {42, 67}, {43, 66}, {11, 100}, {12, 99}, {13, 125}, {14, 126}, {39, 85}, {40, 90}, {13, 126}, {40, 91}, {38, 85}, {14, 125}, {8, 127}, {7, 127}, {16, 105}, {16, 106}, {58, 70}, {59, 71}, {58, 71}, {59, 70}, {37, 91}, {37, 90}, {11, 141}, {7, 128}, {47, 168}, {10, 141}, {8, 128}, {47, 167}, {27, 147}, {26, 146}, {26, 147}, {27, 146}, {5, 143}, {5, 142}, {53, 165}, {54, 166}, {25, 139}, {30, 140}, {25, 138}, {31, 140}, {53, 166}, {54, 165}, {31, 137}, {30, 137}, {48, 167}, {48, 168}, {29, 132}, {10, 144}, {30, 132}, {29, 135}, {28, 134}, {11, 144}, {29, 134}, {28, 135}, {30, 131}, {16, 142}, {29, 131}, {16, 143}, {8, 168}, {9, 168}, {35, 130}, {49, 144}, {35, 129}, {50, 144}, {36, 129}, {35, 133}, {36, 130}, {34, 133}, {14, 166}, {15, 167}, {14, 167}, {15, 166}, {34, 136}, {35, 136}, {9, 165}, {8, 165}, {36, 138}, {36, 139}, {33, 145}, {32, 145}, {32, 148}, {33, 148}, {56, 141}, {56, 142}, {55, 142}, {55, 141}, {57, 131}, {62, 132}, {57, 130}, {63, 132}, {50, 143}, {49, 143}, {63, 129}, {62, 129}, {68, 130}, {68, 131}, {76, 128}, {77, 128}, {114, 160}, {115, 160}, {120, 152}, {120, 153}, {115, 149}, {114, 149}, {73, 161}, {119, 159}, {118, 158}, {74, 162}, {118, 159}, {119, 158}, {113, 155}, {73, 162}, {113, 154}, {74, 161}, {79, 164}, {79, 163}, {117, 153}, {117, 152}, {116, 154}, {116, 155}, {80, 163}, {80, 164} }>;

(II) A more general form is to represent the graph as the orbit of {65, 69} under the group generated by the following permutations:

a: (5, 11)(6, 12)(7, 13)(8, 14)(9, 15)(10, 16)(17, 18)(19, 20)(73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84)(97, 99)(98, 100)(105, 107)(106, 108)(113, 116)(114, 115)(117, 120)(118, 119)(125, 127)(126, 128)(141, 142)(143, 144)(161, 164)(162, 163)(165, 166)(167, 168)
b: (25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(41, 44)(42, 43)(69, 72)(70, 71)(113, 114)(115, 116)(117, 118)(119, 120)(129, 132)(130, 131)(133, 135)(134, 136)(137, 139)(138, 140)(145, 147)(146, 148)(149, 155)(150, 156)(151, 157)(152, 158)(153, 159)(154, 160)(161, 162)(163, 164)
c: (73, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84)(97, 98)(99, 100)(105, 106)(107, 108)(113, 116)(114, 115)(117, 120)(118, 119)(125, 126)(127, 128)(161, 164)(162, 163)
d: (21, 24)(22, 23)(37, 40)(38, 39)(41, 42)(43, 44)(57, 63)(58, 64)(59, 65)(60, 66)(61, 67)(62, 68)(69, 70)(71, 72)(101, 104)(102, 103)(129, 130)(131, 132)
e: (25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(41, 44)(42, 43)(69, 72)(70, 71)(129, 132)(130, 131)(133, 134)(135, 136)(137, 138)(139, 140)(145, 146)(147, 148)
f: (1, 17, 97, 161, 134, 42, 103, 123, 167, 127, 119, 140, 130, 39, 111, 143, 107, 115, 148, 70, 23, 3, 19, 99, 163, 136, 44, 101, 121, 165, 125, 117, 138, 132, 37, 109, 141, 105, 113, 146, 72, 21)(2, 18, 98, 162, 133, 41, 104, 124, 168, 128, 120, 139, 129, 40, 112, 144, 108, 116, 147, 69, 24, 4, 20, 100, 164, 135, 43, 102, 122, 166, 126, 118, 137, 131, 38, 110, 142, 106, 114, 145, 71, 22)(5, 73, 149, 33, 59, 87, 47, 7, 75, 151, 35, 61, 89, 49, 9, 77, 153, 25, 63, 91, 51, 11, 79, 155, 27, 65, 93, 53, 13, 81, 157, 29, 67, 95, 55, 15, 83, 159, 31, 57, 85, 45)(6, 74, 150, 34, 60, 88, 48, 8, 76, 152, 36, 62, 90, 50, 10, 78, 154, 26, 64, 92, 52, 12, 80, 156, 28, 66, 94, 54, 14, 82, 158, 30, 68, 96, 56, 16, 84, 160, 32, 58, 86, 46)
g: (2, 4)(5, 59, 11, 65)(6, 58, 12, 64)(7, 57, 13, 63)(8, 68, 14, 62)(9, 67, 15, 61)(10, 66, 16, 60)(17, 24, 18, 21)(19, 22, 20, 23)(25, 81, 31, 75)(26, 80, 32, 74)(27, 79, 33, 73)(28, 78, 34, 84)(29, 77, 35, 83)(30, 76, 36, 82)(37, 167, 40, 168)(38, 166, 39, 165)(41, 107, 43, 105)(42, 106, 44, 108)(45, 93)(46, 92)(47, 91)(48, 90)(49, 89)(50, 88)(51, 87)(52, 86)(53, 85)(54, 96)(55, 95)(56, 94)(69, 97, 71, 99)(70, 100, 72, 98)(101, 143, 104, 144)(102, 142, 103, 141)(109, 123)(110, 122)(111, 121)(112, 124)(113, 134, 116, 133)(114, 135, 115, 136)(117, 140, 120, 139)(118, 137, 119, 138)(125, 129, 127, 131)(126, 132, 128, 130)(145, 161, 146, 164)(147, 163, 148, 162)(149, 155)(150, 154)(151, 153)(156, 160)(157, 159)
h: (1, 2)(3, 4)(17, 20)(18, 19)(45, 51)(46, 52)(47, 53)(48, 54)(49, 55)(50, 56)(109, 110)(111, 112)(121, 122)(123, 124)(141, 144)(142, 143)(165, 168)(166, 167)
m: (2, 4)(5, 66, 11, 60)(6, 67, 12, 61)(7, 68, 13, 62)(8, 57, 14, 63)(9, 58, 15, 64)(10, 59, 16, 65)(17, 40, 18, 37)(19, 38, 20, 39)(21, 167, 24, 168)(22, 166, 23, 165)(25, 84, 31, 78)(26, 73, 32, 79)(27, 74, 33, 80)(28, 75, 34, 81)(29, 76, 35, 82)(30, 77, 36, 83)(41, 97, 43, 99)(42, 100, 44, 98)(45, 90)(46, 91)(47, 92)(48, 93)(49, 94)(50, 95)(51, 96)(52, 85)(53, 86)(54, 87)(55, 88)(56, 89)(69, 107, 71, 105)(70, 106, 72, 108)(101, 141, 104, 142)(102, 144, 103, 143)(110, 112)(113, 137, 115, 139)(114, 140, 116, 138)(117, 135, 119, 133)(118, 134, 120, 136)(122, 124)(125, 129, 127, 131)(126, 132, 128, 130)(145, 163, 147, 161)(146, 162, 148, 164)(149, 152, 155, 158)(150, 153, 156, 159)(151, 154, 157, 160)

(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
C4[ 168, 32 ]
168
-1 52 85 53 86
-2 46 47 85 86
-3 46 47 91 92
-4 91 92 52 53
-5 143 97 98 142
-6 18 19 97 98
-7 127 18 128 19
-8 165 168 127 128
-9 165 168 107 108
-10 144 107 108 141
-11 99 100 144 141
-12 99 100 17 20
-13 125 126 17 20
-14 166 167 125 126
-15 166 167 105 106
-16 143 105 106 142
-17 12 45 13 46
-18 45 46 6 7
-19 6 7 51 52
-20 12 13 51 52
-21 57 58 92 93
-22 57 58 86 87
-23 63 64 86 87
-24 92 93 63 64
-25 69 70 138 139
-26 69 146 70 147
-27 44 146 147 43
-28 44 134 135 43
-29 132 134 135 131
-30 132 137 140 131
-31 71 137 72 140
-32 145 71 148 72
-33 145 148 41 42
-34 133 136 41 42
-35 133 136 129 130
-36 138 139 129 130
-37 67 68 90 91
-38 67 68 85 96
-39 61 62 85 96
-40 90 91 61 62
-41 33 34 60 61
-42 33 66 34 67
-43 66 67 27 28
-44 27 60 28 61
-45 110 111 17 18
-46 2 3 17 18
-47 2 167 3 168
-48 121 167 124 168
-49 121 143 144 124
-50 143 144 112 109
-51 112 19 20 109
-52 1 4 19 20
-53 165 1 166 4
-54 165 122 166 123
-55 122 123 141 142
-56 110 111 141 142
-57 22 130 21 131
-58 22 70 71 21
-59 70 103 71 104
-60 44 103 104 41
-61 44 39 40 41
-62 132 39 40 129
-63 132 23 24 129
-64 23 24 69 72
-65 101 69 102 72
-66 101 102 42 43
-67 37 38 42 43
-68 37 38 130 131
-69 25 26 64 65
-70 25 58 26 59
-71 58 59 31 32
-72 31 64 32 65
-73 106 161 107 162
-74 99 161 162 98
-75 99 119 98 120
-76 125 128 119 120
-77 125 115 116 128
-78 115 105 116 108
-79 105 108 163 164
-80 100 97 163 164
-81 100 117 118 97
-82 126 127 117 118
-83 113 114 126 127
-84 113 114 106 107
-85 1 2 38 39
-86 22 1 23 2
-87 22 23 123 124
-88 101 123 124 104
-89 111 101 112 104
-90 111 112 37 40
-91 3 4 37 40
-92 24 3 4 21
-93 121 122 24 21
-94 121 122 102 103
-95 110 102 103 109
-96 110 38 39 109
-97 80 81 5 6
-98 5 6 74 75
-99 11 12 74 75
-100 11 12 80 81
-101 66 88 89 65
-102 66 94 95 65
-103 59 60 94 95
-104 88 89 59 60
-105 78 79 15 16
-106 15 16 73 84
-107 73 84 9 10
-108 78 79 9 10
-109 50 51 95 96
-110 45 56 95 96
-111 45 56 89 90
-112 89 90 50 51
-113 154 155 83 84
-114 83 149 160 84
-115 77 78 149 160
-116 77 154 78 155
-117 81 82 152 153
-118 81 158 82 159
-119 158 159 75 76
-120 75 152 76 153
-121 48 49 93 94
-122 55 93 94 54
-123 55 88 54 87
-124 88 48 49 87
-125 77 13 14 76
-126 13 14 82 83
-127 82 83 7 8
-128 77 7 8 76
-129 35 36 62 63
-130 35 57 68 36
-131 57 68 29 30
-132 29 62 30 63
-133 34 35 149 150
-134 28 149 29 150
-135 155 156 28 29
-136 34 155 35 156
-137 157 158 30 31
-138 25 36 157 158
-139 25 36 151 152
-140 30 151 31 152
-141 11 55 56 10
-142 55 56 5 16
-143 5 16 49 50
-144 11 49 50 10
-145 33 159 160 32
-146 26 27 159 160
-147 154 26 27 153
-148 33 154 32 153
-149 133 134 114 115
-150 133 134 162 163
-151 139 140 162 163
-152 117 139 140 120
-153 147 148 117 120
-154 113 147 148 116
-155 113 135 136 116
-156 135 136 161 164
-157 137 138 161 164
-158 137 138 118 119
-159 145 146 118 119
-160 145 146 114 115
-161 156 157 73 74
-162 73 150 74 151
-163 79 80 150 151
-164 79 156 80 157
-165 8 9 53 54
-166 14 15 53 54
-167 14 47 15 48
-168 47 48 8 9
0

**************