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On this page are computer-accessible forms for the graph C4[ 128, 6 ] = PS(16,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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