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On this page are computer-accessible forms for the graph C4[ 168, 49 ] = UG(ATD[168,79]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 65} under the group generated by the following permutations:

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

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

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