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On this page are computer-accessible forms for the graph C4[ 168, 41 ] = UG(ATD[168,65]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {58, 59} under the group generated by the following permutations:

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

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