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On this page are computer-accessible forms for the graph C4[ 128, 55 ] = SS[128,16].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

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

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

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