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On this page are computer-accessible forms for the graph C4[ 160, 54 ] = UG(ATD[160,68]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 9} under the group generated by the following permutations:

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

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

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