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

On this page are computer-accessible forms for the graph C4[ 108, 20 ] = UG(ATD[108,27]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {84, 85} under the group generated by the following permutations:

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

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

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