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

On this page are computer-accessible forms for the graph C4[ 128, 30 ] = UG(ATD[128,7]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {104, 105} under the group generated by the following permutations:

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

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

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