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On this page are computer-accessible forms for the graph C4[ 168, 34 ] = UG(ATD[168,1]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 2} under the group generated by the following permutations:

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

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