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On this page are computer-accessible forms for the graph C4[ 128, 35 ] = UG(ATD[128,52]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {112, 113} under the group generated by the following permutations:

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

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

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