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On this page are computer-accessible forms for the graph C4[ 128, 32 ] = UG(ATD[128,42]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {124, 126} under the group generated by the following permutations:

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

**************

&Graph
C4[ 128, 32 ]
128
-1 13 5 9 10
-2 66 77 5 65
-3 55 13 101 53
-4 77 101 125 127
-5 1 2 25 17
-6 49 17 50 105
-7 25 91 29 31
-8 121 123 91 105
-9 22 1 29 21
-10 1 37 38 49
-11 121 81 83 29
-12 121 111 49 109
-13 1 3 26 19
-14 89 26 29 30
-15 49 51 19 107
-16 121 89 122 107
-17 33 45 5 6
-18 33 77 78 118
-19 45 13 15 59
-20 101 59 103 118
-21 41 9 42 53
-22 66 69 70 9
-23 99 127 53 97
-24 66 115 116 127
-25 35 46 5 7
-26 13 46 57 14
-27 77 35 79 120
-28 57 101 102 120
-29 11 14 7 9
-30 14 102 53 54
-31 66 68 79 7
-32 79 102 127 128
-33 17 61 18 73
-34 61 94 105 106
-35 25 27 73 87
-36 91 92 94 87
-37 69 71 10 65
-38 44 55 42 10
-39 114 125 116 65
-40 55 99 100 125
-41 81 61 62 21
-42 38 93 94 21
-43 111 81 73 75
-44 88 111 38 87
-45 17 19 63 74
-46 25 26 74 85
-47 105 63 96 107
-48 89 91 85 96
-49 12 15 6 10
-50 67 78 6 65
-51 55 56 15 103
-52 78 103 125 126
-53 23 3 30 21
-54 122 81 82 30
-55 3 38 40 51
-56 111 122 112 51
-57 26 28 86 76
-58 89 90 95 86
-59 19 20 64 76
-60 95 107 64 108
-61 33 34 41 97
-62 70 117 41 118
-63 45 47 115 97
-64 59 70 60 115
-65 2 37 39 50
-66 22 2 24 31
-67 110 123 50 109
-68 123 83 84 31
-69 22 37 93 95
-70 22 83 62 64
-71 88 37 86 109
-72 83 75 76 109
-73 33 35 43 98
-74 45 46 113 98
-75 72 118 43 120
-76 57 113 59 72
-77 2 4 27 18
-78 50 18 106 52
-79 92 27 31 32
-80 123 124 92 106
-81 11 41 43 54
-82 128 97 54 98
-83 11 68 70 72
-84 68 113 115 128
-85 100 46 48 114
-86 57 58 114 71
-87 44 100 35 36
-88 44 71 119 120
-89 14 58 48 16
-90 58 102 104 119
-91 36 48 7 8
-92 79 36 80 119
-93 69 117 42 119
-94 99 34 36 42
-95 58 69 60 116
-96 99 47 48 116
-97 23 82 61 63
-98 112 82 73 74
-99 23 94 40 96
-100 112 40 85 87
-101 3 4 28 20
-102 90 28 30 32
-103 51 52 20 108
-104 122 90 124 108
-105 34 47 6 8
-106 34 78 80 117
-107 47 15 16 60
-108 103 60 104 117
-109 12 67 71 72
-110 67 113 114 126
-111 44 12 56 43
-112 56 100 126 98
-113 110 84 74 76
-114 110 39 85 86
-115 24 84 63 64
-116 24 39 95 96
-117 93 62 106 108
-118 18 62 20 75
-119 88 90 92 93
-120 88 27 28 75
-121 11 12 16 8
-122 56 16 104 54
-123 67 68 80 8
-124 80 104 126 128
-125 4 39 40 52
-126 110 112 124 52
-127 23 24 4 32
-128 124 82 84 32
0

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