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

On this page are computer-accessible forms for the graph C4[ 111, 2 ] = PS(3,37;10).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {37, 38} under the group generated by the following permutations:

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

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

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