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On this page are computer-accessible forms for the graph C4[ 168, 48 ] = UG(ATD[168,77]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {21, 28} under the group generated by the following permutations:

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

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

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