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On this page are computer-accessible forms for the graph C4[ 168, 45 ] = UG(ATD[168,72]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {104, 107} under the group generated by the following permutations:

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

(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.

**************

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

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