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

On this page are computer-accessible forms for the graph C4[ 128, 11 ] = MPS(4,64;15).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 72} under the group generated by the following permutations:

a: (7, 23)(38, 126)(39, 111)(54, 110)(55, 127)(79, 95)
b: (11, 27)(42, 98)(43, 115)(58, 114)(59, 99)(67, 83)
c: (5, 21)(36, 124)(37, 109)(52, 108)(53, 125)(77, 93)
d: (14, 30)(45, 101)(46, 118)(61, 117)(62, 102)(70, 86)
e: (5, 77)(21, 93)(36, 124)(52, 108)
f: (9, 25)(40, 128)(41, 113)(56, 112)(57, 97)(65, 81)
g: (13, 69)(29, 85)(45, 117)(61, 101)
h: (4, 20)(35, 123)(36, 108)(51, 107)(52, 124)(76, 92)
m: (6, 78)(22, 94)(37, 125)(53, 109)
n1: (11, 67)(27, 83)(43, 115)(59, 99)
a1: (16, 32)(47, 103)(48, 120)(63, 119)(64, 104)(72, 88)
b1: (12, 68)(28, 84)(44, 116)(60, 100)
c1: (8, 80)(24, 96)(39, 127)(55, 111)
d1: (10, 66)(26, 82)(42, 114)(58, 98)
e1: (1, 2)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(17, 18)(19, 32)(20, 31)(21, 30)(22, 29)(23, 28)(24, 27)(25, 26)(34, 104)(35, 47)(36, 46)(37, 45)(38, 44)(39, 43)(40, 42)(48, 106)(50, 120)(51, 63)(52, 62)(53, 61)(54, 60)(55, 59)(56, 58)(64, 122)(65, 82)(66, 81)(67, 80)(68, 79)(69, 78)(70, 77)(71, 76)(72, 75)(73, 90)(74, 89)(83, 96)(84, 95)(85, 94)(86, 93)(87, 92)(88, 91)(97, 113)(98, 112)(99, 111)(100, 110)(101, 109)(102, 108)(103, 107)(105, 121)(114, 128)(115, 127)(116, 126)(117, 125)(118, 124)(119, 123)
f1: (14, 70)(30, 86)(46, 118)(62, 102)
g1: (10, 26)(41, 97)(42, 114)(57, 113)(58, 98)(66, 82)
h1: (2, 16)(3, 15)(4, 14)(5, 13)(6, 12)(7, 11)(8, 10)(18, 32)(19, 31)(20, 30)(21, 29)(22, 28)(23, 27)(24, 26)(33, 104)(34, 47)(35, 46)(36, 45)(37, 44)(38, 43)(39, 42)(40, 41)(48, 105)(49, 120)(50, 63)(51, 62)(52, 61)(53, 60)(54, 59)(55, 58)(56, 57)(64, 121)(65, 81)(66, 80)(67, 79)(68, 78)(69, 77)(70, 76)(71, 75)(72, 74)(73, 89)(82, 96)(83, 95)(84, 94)(85, 93)(86, 92)(87, 91)(88, 90)(97, 112)(98, 111)(99, 110)(100, 109)(101, 108)(102, 107)(103, 106)(113, 128)(114, 127)(115, 126)(116, 125)(117, 124)(118, 123)(119, 122)
m1: (16, 72)(32, 88)(48, 120)(64, 104)
n2: (3, 19)(34, 122)(35, 107)(50, 106)(51, 123)(75, 91)
a2: (3, 75)(19, 91)(34, 122)(50, 106)
b2: (9, 65)(25, 81)(41, 113)(57, 97)
c2: (6, 22)(37, 125)(38, 110)(53, 109)(54, 126)(78, 94)
d2: (15, 31)(46, 102)(47, 119)(62, 118)(63, 103)(71, 87)
e2: (1, 33, 2, 34, 3, 35, 4, 36, 5, 37, 6, 38, 7, 39, 8, 40, 9, 41, 10, 42, 11, 43, 12, 44, 13, 45, 14, 46, 15, 47, 16, 48, 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)(65, 97, 66, 98, 67, 99, 68, 100, 69, 101, 70, 102, 71, 103, 72, 104, 73, 105, 74, 106, 75, 107, 76, 108, 77, 109, 78, 110, 79, 111, 80, 112, 81, 113, 82, 114, 83, 115, 84, 116, 85, 117, 86, 118, 87, 119, 88, 120, 89, 121, 90, 122, 91, 123, 92, 124, 93, 125, 94, 126, 95, 127, 96, 128)
f2: (15, 71)(31, 87)(47, 119)(63, 103)
g2: (12, 28)(43, 99)(44, 116)(59, 115)(60, 100)(68, 84)
h2: (4, 76)(20, 92)(35, 123)(51, 107)
m2: (8, 24)(39, 127)(40, 112)(55, 111)(56, 128)(80, 96)
n3: (7, 79)(23, 95)(38, 126)(54, 110)
a3: (13, 29)(44, 100)(45, 117)(60, 116)(61, 101)(69, 85)

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

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