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On this page are computer-accessible forms for the graph C4[ 168, 52 ] = UG(ATD[168,82]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 69} under the group generated by the following permutations:

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

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

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