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On this page are computer-accessible forms for the graph C4[ 168, 43 ] = UG(ATD[168,68]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {35, 43} under the group generated by the following permutations:

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

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