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On this page are computer-accessible forms for the graph C4[ 168, 38 ] = UG(ATD[168,62]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {54, 55} under the group generated by the following permutations:

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

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

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