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On this page are computer-accessible forms for the graph C4[ 128, 8 ] = PS(8,32;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 34} under the group generated by the following permutations:

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

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