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On this page are computer-accessible forms for the graph C4[ 128, 39 ] = UG(ATD[128,63]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 17} under the group generated by the following permutations:

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

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

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