[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 128, 7 ] = MPS(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}, {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}, {99, 107}, {3, 10}, {103, 110}, {101, 108}, {39, 46}, {5, 12}, {7, 14}, {35, 42}, {37, 44}, {67, 74}, {69, 76}, {71, 78}, {99, 106}, {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}, {54, 57}, {50, 61}, {18, 29}, {22, 25}, {36, 43}, {68, 75}, {82, 93}, {86, 89}, {100, 107}, {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, 121}, {58, 72}, {52, 64}, {53, 64}, {61, 72}, {8, 126}, {2, 123}, {4, 125}, {6, 127}, {3, 121}, {59, 65}, {6, 124}, {7, 125}, {62, 68}, {63, 69}, {1, 122}, {60, 71}, {5, 126}, {57, 68}, {59, 70}, {63, 66}, {1, 127}, {61, 67}, {60, 66}, {57, 71}, {4, 122}, {5, 123}, {3, 124}, {58, 69}, {62, 65}, {2, 128}, {7, 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: (1, 9, 24, 28, 39, 47, 54, 58, 69, 77, 84, 96, 99, 107, 114, 126, 5, 13, 20, 32, 35, 43, 50, 62, 65, 73, 88, 92, 103, 111, 118, 122)(2, 14, 17, 25, 40, 44, 55, 63, 70, 74, 85, 93, 100, 112, 115, 123, 6, 10, 21, 29, 36, 48, 51, 59, 66, 78, 81, 89, 104, 108, 119, 127)(3, 11, 18, 30, 33, 41, 56, 60, 71, 79, 86, 90, 101, 109, 116, 128, 7, 15, 22, 26, 37, 45, 52, 64, 67, 75, 82, 94, 97, 105, 120, 124)(4, 16, 19, 27, 34, 46, 49, 57, 72, 76, 87, 95, 102, 106, 117, 125, 8, 12, 23, 31, 38, 42, 53, 61, 68, 80, 83, 91, 98, 110, 113, 121)
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, 8)(3, 7)(4, 6)(9, 16)(10, 15)(11, 14)(12, 13)(18, 24)(19, 23)(20, 22)(25, 32)(26, 31)(27, 30)(28, 29)(34, 40)(35, 39)(36, 38)(41, 48)(42, 47)(43, 46)(44, 45)(50, 56)(51, 55)(52, 54)(57, 64)(58, 63)(59, 62)(60, 61)(66, 72)(67, 71)(68, 70)(73, 80)(74, 79)(75, 78)(76, 77)(82, 88)(83, 87)(84, 86)(89, 96)(90, 95)(91, 94)(92, 93)(98, 104)(99, 103)(100, 102)(105, 112)(106, 111)(107, 110)(108, 109)(114, 120)(115, 119)(116, 118)(121, 128)(122, 127)(123, 126)(124, 125)
d: (2, 6)(4, 8)(9, 127)(10, 124)(11, 121)(12, 126)(13, 123)(14, 128)(15, 125)(16, 122)(17, 113)(18, 118)(19, 115)(20, 120)(21, 117)(22, 114)(23, 119)(24, 116)(25, 107)(26, 112)(27, 109)(28, 106)(29, 111)(30, 108)(31, 105)(32, 110)(33, 101)(34, 98)(35, 103)(36, 100)(37, 97)(38, 102)(39, 99)(40, 104)(41, 95)(42, 92)(43, 89)(44, 94)(45, 91)(46, 96)(47, 93)(48, 90)(49, 81)(50, 86)(51, 83)(52, 88)(53, 85)(54, 82)(55, 87)(56, 84)(57, 75)(58, 80)(59, 77)(60, 74)(61, 79)(62, 76)(63, 73)(64, 78)(65, 69)(67, 71)

(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.

**************

&Graph
C4[ 128, 7 ]
128
-1 122 16 127 9
-2 123 128 9 10
-3 11 121 124 10
-4 11 12 122 125
-5 12 13 123 126
-6 13 14 124 127
-7 14 15 125 128
-8 121 15 16 126
-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 3 117 8 118
-122 1 4 118 119
-123 2 5 119 120
-124 3 113 6 120
-125 113 4 114 7
-126 114 5 115 8
-127 1 115 6 116
-128 2 116 7 117
0

**************