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

On this page are computer-accessible forms for the graph C4[ 135, 5 ] = PS(3,45;14).

(I) Following is a form readable by MAGMA:

g:=Graph<135|{ {45, 46}, {80, 94}, {81, 95}, {78, 92}, {79, 93}, {77, 91}, {64, 95}, {65, 96}, {89, 120}, {87, 118}, {85, 116}, {83, 114}, {81, 112}, {79, 110}, {77, 108}, {67, 98}, {69, 100}, {71, 102}, {73, 104}, {75, 106}, {66, 97}, {90, 121}, {86, 117}, {82, 113}, {78, 109}, {70, 101}, {74, 105}, {68, 99}, {84, 115}, {76, 107}, {2, 46}, {3, 47}, {16, 60}, {17, 61}, {18, 62}, {19, 63}, {1, 47}, {16, 62}, {17, 63}, {72, 103}, {88, 119}, {2, 48}, {90, 104}, {87, 101}, {86, 100}, {83, 97}, {82, 96}, {3, 49}, {6, 52}, {7, 53}, {10, 56}, {11, 57}, {14, 60}, {15, 61}, {4, 48}, {5, 49}, {6, 50}, {7, 51}, {12, 56}, {13, 57}, {14, 58}, {15, 59}, {4, 50}, {85, 99}, {84, 98}, {5, 51}, {12, 58}, {13, 59}, {64, 123}, {68, 127}, {8, 52}, {9, 53}, {10, 54}, {11, 55}, {65, 124}, {67, 126}, {8, 54}, {89, 103}, {88, 102}, {9, 55}, {66, 125}, {80, 111}, {31, 92}, {35, 96}, {39, 100}, {43, 104}, {30, 91}, {36, 97}, {38, 99}, {44, 105}, {47, 106}, {53, 112}, {55, 114}, {61, 120}, {63, 122}, {37, 98}, {45, 106}, {46, 105}, {54, 113}, {62, 121}, {17, 91}, {33, 107}, {32, 106}, {21, 95}, {20, 94}, {36, 110}, {37, 111}, {56, 115}, {60, 119}, {48, 124}, {49, 125}, {50, 126}, {51, 127}, {40, 101}, {42, 103}, {57, 116}, {59, 118}, {18, 92}, {19, 93}, {34, 108}, {35, 109}, {41, 102}, {58, 117}, {18, 64}, {31, 77}, {30, 76}, {27, 73}, {26, 72}, {23, 69}, {22, 68}, {19, 65}, {20, 64}, {31, 75}, {30, 74}, {29, 73}, {28, 72}, {23, 67}, {22, 66}, {21, 65}, {46, 122}, {47, 123}, {20, 66}, {29, 75}, {28, 74}, {21, 67}, {38, 112}, {39, 113}, {40, 114}, {41, 115}, {44, 118}, {45, 119}, {1, 90}, {48, 107}, {52, 111}, {24, 68}, {27, 71}, {26, 70}, {25, 69}, {49, 108}, {51, 110}, {24, 70}, {25, 71}, {42, 116}, {43, 117}, {50, 109}, {61, 92}, {63, 94}, {62, 93}, {60, 91}, {1, 107}, {21, 127}, {4, 110}, {5, 111}, {16, 122}, {17, 123}, {20, 126}, {32, 76}, {34, 78}, {33, 77}, {35, 79}, {2, 108}, {33, 79}, {32, 78}, {3, 109}, {18, 124}, {19, 125}, {34, 80}, {35, 81}, {38, 84}, {39, 85}, {42, 88}, {43, 89}, {36, 80}, {37, 81}, {38, 82}, {39, 83}, {44, 88}, {45, 89}, {6, 112}, {31, 105}, {30, 104}, {23, 97}, {22, 96}, {7, 113}, {14, 120}, {15, 121}, {36, 82}, {37, 83}, {44, 90}, {8, 127}, {1, 120}, {3, 122}, {5, 124}, {7, 126}, {8, 114}, {29, 103}, {28, 102}, {25, 99}, {24, 98}, {9, 115}, {12, 118}, {13, 119}, {2, 121}, {6, 125}, {40, 84}, {41, 85}, {42, 86}, {43, 87}, {32, 93}, {34, 95}, {10, 116}, {27, 101}, {26, 100}, {11, 117}, {40, 86}, {41, 87}, {4, 123}, {33, 94}, {9, 128}, {11, 130}, {13, 132}, {15, 134}, {10, 129}, {14, 133}, {12, 131}, {22, 128}, {23, 129}, {16, 135}, {24, 130}, {29, 135}, {28, 134}, {25, 131}, {26, 132}, {27, 133}, {52, 128}, {53, 129}, {54, 130}, {55, 131}, {56, 132}, {57, 133}, {58, 134}, {59, 135}, {69, 128}, {71, 130}, {70, 129}, {72, 131}, {76, 135}, {73, 132}, {75, 134}, {74, 133} }>;

(II) A more general form is to represent the graph as the orbit of {45, 46} under the group generated by the following permutations:

a: (1, 46, 91)(2, 60, 107, 45, 77, 120)(3, 74, 123, 44, 63, 104)(4, 88, 94, 43, 49, 133)(5, 57, 110, 42, 80, 117)(6, 71, 126, 41, 66, 101)(7, 85, 97, 40, 52, 130)(8, 54, 113, 39, 83, 114)(9, 68, 129, 38, 69, 98)(10, 82, 100, 37, 55, 127)(11, 51, 116, 36, 86, 111)(12, 65, 132, 35, 72, 95)(13, 79, 103, 34, 58, 124)(14, 48, 119, 33, 89, 108)(15, 62, 135, 32, 75, 92)(16, 76, 106, 31, 61, 121)(17, 90, 122, 30, 47, 105)(18, 59, 93, 29, 78, 134)(19, 73, 109, 28, 64, 118)(20, 87, 125, 27, 50, 102)(21, 56, 96, 26, 81, 131)(22, 70, 112, 25, 67, 115)(23, 84, 128, 24, 53, 99)
b: (2, 45)(3, 44)(4, 43)(5, 42)(6, 41)(7, 40)(8, 39)(9, 38)(10, 37)(11, 36)(12, 35)(13, 34)(14, 33)(15, 32)(16, 31)(17, 30)(18, 29)(19, 28)(20, 27)(21, 26)(22, 25)(23, 24)(47, 90)(48, 89)(49, 88)(50, 87)(51, 86)(52, 85)(53, 84)(54, 83)(55, 82)(56, 81)(57, 80)(58, 79)(59, 78)(60, 77)(61, 76)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)(92, 135)(93, 134)(94, 133)(95, 132)(96, 131)(97, 130)(98, 129)(99, 128)(100, 127)(101, 126)(102, 125)(103, 124)(104, 123)(105, 122)(106, 121)(107, 120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)
c: (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, 129, 130, 131, 132, 133, 134, 135)

(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[ 135, 5 ]
135
-1 90 47 107 120
-2 121 46 48 108
-3 122 47 49 109
-4 110 123 48 50
-5 111 124 49 51
-6 112 125 50 52
-7 113 126 51 53
-8 114 127 52 54
-9 55 115 128 53
-10 56 116 129 54
-11 55 57 117 130
-12 56 58 118 131
-13 132 57 59 119
-14 133 58 60 120
-15 121 134 59 61
-16 122 135 60 62
-17 123 91 61 63
-18 124 92 62 64
-19 125 93 63 65
-20 66 126 94 64
-21 67 127 95 65
-22 66 68 128 96
-23 67 69 129 97
-24 68 70 130 98
-25 99 69 71 131
-26 132 100 70 72
-27 133 101 71 73
-28 134 102 72 74
-29 135 103 73 75
-30 91 104 74 76
-31 77 92 105 75
-32 78 93 106 76
-33 77 79 94 107
-34 78 80 95 108
-35 79 81 96 109
-36 110 80 82 97
-37 111 81 83 98
-38 99 112 82 84
-39 100 113 83 85
-40 101 114 84 86
-41 102 115 85 87
-42 88 103 116 86
-43 89 104 117 87
-44 88 90 105 118
-45 89 46 106 119
-46 45 122 2 105
-47 1 123 3 106
-48 2 124 4 107
-49 3 125 5 108
-50 4 126 6 109
-51 110 5 127 7
-52 111 6 128 8
-53 112 7 129 9
-54 113 8 130 10
-55 11 114 9 131
-56 132 12 115 10
-57 11 133 13 116
-58 12 134 14 117
-59 13 135 15 118
-60 14 91 16 119
-61 15 92 17 120
-62 121 16 93 18
-63 122 17 94 19
-64 123 18 95 20
-65 124 19 96 21
-66 22 125 20 97
-67 23 126 21 98
-68 22 99 24 127
-69 23 100 25 128
-70 24 101 26 129
-71 25 102 27 130
-72 26 103 28 131
-73 132 27 104 29
-74 133 28 105 30
-75 134 29 106 31
-76 135 30 107 32
-77 33 91 31 108
-78 34 92 32 109
-79 33 110 35 93
-80 34 111 36 94
-81 35 112 37 95
-82 36 113 38 96
-83 37 114 39 97
-84 38 115 40 98
-85 99 39 116 41
-86 100 40 117 42
-87 101 41 118 43
-88 44 102 42 119
-89 45 103 43 120
-90 44 121 1 104
-91 77 60 17 30
-92 78 61 18 31
-93 79 62 19 32
-94 33 80 63 20
-95 34 81 64 21
-96 22 35 82 65
-97 66 23 36 83
-98 67 24 37 84
-99 68 25 38 85
-100 69 26 39 86
-101 70 27 40 87
-102 88 71 28 41
-103 89 72 29 42
-104 90 73 30 43
-105 44 46 74 31
-106 45 47 75 32
-107 33 1 48 76
-108 77 34 2 49
-109 78 35 3 50
-110 79 36 4 51
-111 80 37 5 52
-112 81 38 6 53
-113 82 39 7 54
-114 55 83 40 8
-115 56 84 41 9
-116 57 85 42 10
-117 11 58 86 43
-118 44 12 59 87
-119 88 45 13 60
-120 1 89 14 61
-121 2 90 15 62
-122 46 3 16 63
-123 47 4 17 64
-124 48 5 18 65
-125 66 49 6 19
-126 67 50 7 20
-127 68 51 8 21
-128 22 69 52 9
-129 23 70 53 10
-130 11 24 71 54
-131 55 12 25 72
-132 56 13 26 73
-133 57 14 27 74
-134 58 15 28 75
-135 59 16 29 76
0

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