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On this page are computer-accessible forms for the graph C4[ 128, 9 ] = PS(8,32;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 36} under the group generated by the following permutations:

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

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

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