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On this page are computer-accessible forms for the graph C4[ 128, 41 ] = UG(ATD[128,69]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 11} under the group generated by the following permutations:

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

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

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