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

On this page are computer-accessible forms for the graph C4[ 108, 13 ] = AMC(3,12,[1.1:9.10]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {72, 78} under the group generated by the following permutations:

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

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

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