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On this page are computer-accessible forms for the graph C4[ 128, 40 ] = UG(ATD[128,66]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 33} under the group generated by the following permutations:

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

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

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