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On this page are computer-accessible forms for the graph C4[ 168, 33 ] = PL(BC_42({0,21},{1,34}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {140, 143} under the group generated by the following permutations:

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

(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.

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

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