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On this page are computer-accessible forms for the graph C4[ 128, 16 ] = PL(MSY(8,8,3,0)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 113} under the group generated by the following permutations:

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

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

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