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On this page are computer-accessible forms for the graph C4[ 128, 37 ] = UG(ATD[128,57]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {38, 39} under the group generated by the following permutations:

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

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

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