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On this page are computer-accessible forms for the graph C4[ 128, 17 ] = MSY(8,16,9,8).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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