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On this page are computer-accessible forms for the graph C4[ 128, 31 ] = UG(ATD[128,21]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {14, 15} under the group generated by the following permutations:

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

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

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