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

On this page are computer-accessible forms for the graph C4[ 136, 8 ] = PS(8,17;5).

(I) Following is a form readable by MAGMA:

g:=Graph<136|{ {17, 18}, {100, 103}, {82, 86}, {83, 87}, {32, 37}, {34, 39}, {64, 70}, {65, 71}, {33, 38}, {48, 56}, {51, 59}, {50, 58}, {49, 57}, {48, 57}, {50, 59}, {66, 72}, {67, 73}, {49, 58}, {64, 75}, {68, 79}, {32, 44}, {34, 46}, {33, 45}, {84, 88}, {85, 89}, {65, 76}, {67, 78}, {80, 93}, {82, 95}, {101, 104}, {68, 74}, {119, 121}, {118, 120}, {96, 110}, {97, 111}, {51, 60}, {66, 77}, {81, 94}, {102, 105}, {112, 127}, {2, 18}, {3, 19}, {4, 20}, {5, 21}, {6, 22}, {7, 23}, {8, 24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14, 30}, {15, 31}, {105, 120}, {107, 122}, {109, 124}, {111, 126}, {1, 19}, {4, 22}, {5, 23}, {8, 26}, {9, 27}, {12, 30}, {13, 31}, {98, 112}, {99, 113}, {102, 116}, {75, 88}, {79, 92}, {104, 123}, {106, 121}, {108, 127}, {110, 125}, {96, 116}, {97, 117}, {98, 118}, {99, 119}, {72, 93}, {74, 95}, {76, 89}, {78, 91}, {105, 124}, {107, 126}, {2, 20}, {3, 21}, {10, 28}, {11, 29}, {100, 114}, {101, 115}, {47, 56}, {73, 94}, {77, 90}, {106, 125}, {108, 123}, {44, 52}, {47, 55}, {46, 54}, {45, 53}, {36, 61}, {46, 55}, {44, 53}, {38, 63}, {36, 62}, {37, 63}, {37, 62}, {45, 54}, {71, 92}, {70, 91}, {74, 87}, {103, 122}, {6, 24}, {35, 61}, {7, 25}, {35, 60}, {43, 52}, {69, 90}, {73, 86}, {87, 118}, {70, 100}, {71, 101}, {1, 34}, {19, 48}, {86, 117}, {20, 49}, {22, 51}, {69, 99}, {21, 50}, {26, 48}, {27, 49}, {75, 96}, {79, 100}, {92, 112}, {93, 113}, {94, 114}, {95, 115}, {76, 97}, {78, 99}, {14, 32}, {29, 51}, {28, 50}, {15, 33}, {72, 102}, {77, 98}, {88, 119}, {16, 32}, {17, 33}, {16, 34}, {90, 104}, {91, 105}, {94, 108}, {95, 109}, {83, 96}, {23, 35}, {31, 43}, {30, 42}, {29, 41}, {28, 40}, {88, 108}, {89, 109}, {90, 110}, {91, 111}, {80, 101}, {84, 97}, {24, 46}, {25, 47}, {92, 106}, {93, 107}, {81, 102}, {85, 98}, {18, 40}, {19, 41}, {22, 44}, {23, 45}, {31, 36}, {24, 36}, {25, 37}, {26, 38}, {27, 39}, {86, 106}, {87, 107}, {18, 47}, {30, 35}, {20, 42}, {21, 43}, {89, 103}, {52, 80}, {55, 83}, {54, 82}, {53, 81}, {38, 64}, {39, 65}, {39, 64}, {40, 65}, {61, 84}, {59, 82}, {57, 80}, {42, 67}, {40, 66}, {41, 67}, {41, 66}, {58, 81}, {62, 85}, {56, 84}, {57, 85}, {16, 125}, {42, 68}, {17, 126}, {60, 83}, {43, 68}, {8, 120}, {9, 121}, {10, 122}, {11, 123}, {12, 124}, {13, 125}, {14, 126}, {15, 127}, {11, 120}, {15, 124}, {12, 121}, {61, 72}, {14, 123}, {63, 74}, {13, 122}, {62, 73}, {56, 79}, {53, 76}, {55, 78}, {63, 69}, {54, 77}, {60, 71}, {59, 70}, {1, 127}, {52, 75}, {58, 69}, {2, 131}, {4, 133}, {6, 135}, {2, 128}, {3, 129}, {6, 132}, {7, 133}, {10, 136}, {1, 130}, {5, 134}, {4, 130}, {5, 131}, {3, 132}, {8, 134}, {9, 135}, {7, 136}, {16, 128}, {17, 129}, {103, 135}, {104, 136}, {109, 128}, {111, 130}, {110, 129}, {113, 128}, {119, 134}, {117, 132}, {115, 130}, {112, 131}, {118, 133}, {116, 135}, {114, 129}, {113, 132}, {115, 134}, {114, 133}, {116, 131}, {117, 136} }>;

(II) A more general form is to represent the graph as the orbit of {17, 18} under the group generated by the following permutations:

a: (2, 17)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(19, 34)(20, 33)(21, 32)(22, 31)(23, 30)(24, 29)(25, 28)(26, 27)(36, 51)(37, 50)(38, 49)(39, 48)(40, 47)(41, 46)(42, 45)(43, 44)(53, 68)(54, 67)(55, 66)(56, 65)(57, 64)(58, 63)(59, 62)(60, 61)(70, 85)(71, 84)(72, 83)(73, 82)(74, 81)(75, 80)(76, 79)(77, 78)(87, 102)(88, 101)(89, 100)(90, 99)(91, 98)(92, 97)(93, 96)(94, 95)(104, 119)(105, 118)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(111, 112)(121, 136)(122, 135)(123, 134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)
b: (1, 2)(3, 17)(4, 16)(5, 15)(6, 14)(7, 13)(8, 12)(9, 11)(18, 19)(20, 34)(21, 33)(22, 32)(23, 31)(24, 30)(25, 29)(26, 28)(35, 36)(37, 51)(38, 50)(39, 49)(40, 48)(41, 47)(42, 46)(43, 45)(52, 53)(54, 68)(55, 67)(56, 66)(57, 65)(58, 64)(59, 63)(60, 62)(69, 70)(71, 85)(72, 84)(73, 83)(74, 82)(75, 81)(76, 80)(77, 79)(86, 87)(88, 102)(89, 101)(90, 100)(91, 99)(92, 98)(93, 97)(94, 96)(103, 104)(105, 119)(106, 118)(107, 117)(108, 116)(109, 115)(110, 114)(111, 113)(120, 121)(122, 136)(123, 135)(124, 134)(125, 133)(126, 132)(127, 131)(128, 130)
c: (1, 18, 35, 52, 69, 86, 103, 120)(2, 23, 43, 58, 82, 100, 105, 130, 17, 30, 44, 63, 73, 89, 118, 127)(3, 28, 51, 64, 78, 97, 107, 123, 16, 25, 36, 57, 77, 92, 116, 134)(4, 33, 42, 53, 74, 94, 109, 133, 15, 20, 45, 68, 81, 95, 114, 124)(5, 21, 50, 59, 70, 91, 111, 126, 14, 32, 37, 62, 85, 98, 112, 131)(6, 26, 41, 65, 83, 88, 113, 136, 13, 27, 46, 56, 72, 101, 110, 121)(7, 31, 49, 54, 79, 102, 115, 129, 12, 22, 38, 67, 76, 87, 108, 128)(8, 19, 40, 60, 75, 99, 117, 122, 11, 34, 47, 61, 80, 90, 106, 135)(9, 24, 48, 66, 71, 96, 119, 132, 10, 29, 39, 55, 84, 93, 104, 125)

(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[ 136, 8 ]
136
-1 34 127 19 130
-2 18 128 20 131
-3 132 19 129 21
-4 22 133 20 130
-5 23 134 21 131
-6 22 132 24 135
-7 23 133 25 136
-8 24 134 26 120
-9 121 25 135 27
-10 122 26 136 28
-11 123 27 29 120
-12 121 124 28 30
-13 122 125 29 31
-14 123 126 30 32
-15 33 124 127 31
-16 34 125 128 32
-17 33 126 18 129
-18 2 47 17 40
-19 1 3 48 41
-20 2 4 49 42
-21 3 5 50 43
-22 44 4 6 51
-23 45 35 5 7
-24 46 36 6 8
-25 47 37 7 9
-26 48 38 8 10
-27 11 49 39 9
-28 12 50 40 10
-29 11 13 51 41
-30 12 35 14 42
-31 13 36 15 43
-32 44 14 37 16
-33 45 15 38 17
-34 1 46 16 39
-35 23 60 61 30
-36 24 61 62 31
-37 25 62 63 32
-38 33 26 63 64
-39 34 27 64 65
-40 66 28 18 65
-41 66 67 29 19
-42 67 68 30 20
-43 68 52 31 21
-44 22 52 53 32
-45 33 23 53 54
-46 55 34 24 54
-47 55 56 25 18
-48 56 57 26 19
-49 57 58 27 20
-50 58 59 28 21
-51 22 59 60 29
-52 44 80 75 43
-53 44 45 81 76
-54 77 45 46 82
-55 78 46 47 83
-56 79 47 48 84
-57 80 48 49 85
-58 69 81 49 50
-59 70 82 50 51
-60 35 71 83 51
-61 35 36 72 84
-62 36 37 73 85
-63 69 37 38 74
-64 70 38 39 75
-65 71 39 40 76
-66 77 72 40 41
-67 78 73 41 42
-68 79 74 42 43
-69 99 90 58 63
-70 100 91 59 64
-71 101 92 60 65
-72 66 102 93 61
-73 67 94 62 86
-74 68 95 63 87
-75 88 52 96 64
-76 89 53 97 65
-77 66 90 54 98
-78 55 99 67 91
-79 56 100 68 92
-80 57 101 93 52
-81 58 102 94 53
-82 59 95 86 54
-83 55 60 96 87
-84 88 56 61 97
-85 89 57 62 98
-86 82 73 106 117
-87 83 74 107 118
-88 84 75 108 119
-89 103 85 76 109
-90 77 110 69 104
-91 78 111 70 105
-92 79 112 71 106
-93 80 113 72 107
-94 81 114 73 108
-95 82 115 74 109
-96 110 83 116 75
-97 111 84 117 76
-98 77 112 85 118
-99 78 69 113 119
-100 79 70 103 114
-101 80 71 104 115
-102 81 72 105 116
-103 89 100 122 135
-104 90 101 123 136
-105 91 102 124 120
-106 121 92 125 86
-107 122 93 126 87
-108 88 123 94 127
-109 89 124 95 128
-110 90 125 96 129
-111 91 126 97 130
-112 92 127 98 131
-113 99 132 93 128
-114 100 133 94 129
-115 101 134 95 130
-116 102 135 96 131
-117 132 136 86 97
-118 133 87 98 120
-119 88 99 121 134
-120 11 105 8 118
-121 12 106 9 119
-122 13 103 107 10
-123 11 14 104 108
-124 12 15 105 109
-125 110 13 16 106
-126 111 14 17 107
-127 1 112 15 108
-128 2 113 16 109
-129 110 3 114 17
-130 1 111 4 115
-131 2 112 5 116
-132 3 113 6 117
-133 4 114 7 118
-134 5 115 8 119
-135 103 6 116 9
-136 104 7 117 10
0

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