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On this page are computer-accessible forms for the graph C4[ 128, 15 ] = PL(MSY(4,16,7,8)).

(I) Following is a form readable by MAGMA:

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

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

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

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