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On this page are computer-accessible forms for the graph C4[ 168, 39 ] = UG(ATD[168,63]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {146, 147} under the group generated by the following permutations:

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

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

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