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On this page are computer-accessible forms for the graph C4[ 168, 35 ] = UG(ATD[168,3]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {62, 63} under the group generated by the following permutations:

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

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

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