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On this page are computer-accessible forms for the graph C4[ 128, 54 ] = SS[128,12].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 81} under the group generated by the following permutations:

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

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

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