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On this page are computer-accessible forms for the graph C4[ 128, 29 ] = UG(ATD[128,5]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 41} under the group generated by the following permutations:

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

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

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