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

On this page are computer-accessible forms for the graph C4[ 81, 1 ] = DW(27,3).

(I) Following is a form readable by MAGMA:

g:=Graph<81|{ {54, 55}, {27, 28}, {4, 30}, {37, 63}, {36, 62}, {33, 59}, {32, 58}, {5, 31}, {1, 29}, {35, 63}, {34, 62}, {33, 61}, {32, 60}, {3, 31}, {2, 30}, {2, 28}, {35, 61}, {34, 60}, {3, 29}, {4, 32}, {31, 59}, {30, 58}, {29, 57}, {28, 56}, {15, 43}, {14, 42}, {13, 41}, {12, 40}, {7, 35}, {6, 34}, {5, 33}, {20, 48}, {21, 49}, {22, 50}, {23, 51}, {6, 32}, {31, 57}, {30, 56}, {15, 41}, {14, 40}, {7, 33}, {22, 48}, {23, 49}, {8, 34}, {29, 55}, {13, 39}, {12, 38}, {9, 35}, {24, 50}, {25, 51}, {8, 36}, {27, 55}, {11, 39}, {10, 38}, {9, 37}, {24, 52}, {25, 53}, {26, 54}, {10, 36}, {27, 53}, {11, 37}, {26, 52}, {2, 55}, {10, 63}, {8, 61}, {1, 54}, {9, 62}, {8, 63}, {1, 56}, {7, 62}, {5, 60}, {3, 58}, {16, 42}, {17, 43}, {20, 46}, {21, 47}, {2, 57}, {7, 60}, {6, 61}, {3, 56}, {16, 44}, {17, 45}, {18, 46}, {19, 47}, {4, 57}, {6, 59}, {18, 44}, {19, 45}, {4, 59}, {5, 58}, {9, 64}, {15, 70}, {13, 68}, {11, 66}, {25, 80}, {10, 65}, {27, 80}, {26, 81}, {15, 68}, {14, 69}, {11, 64}, {12, 65}, {28, 81}, {14, 67}, {12, 67}, {13, 66}, {1, 81}, {16, 69}, {26, 79}, {18, 71}, {24, 77}, {16, 71}, {17, 70}, {24, 79}, {25, 78}, {17, 72}, {19, 74}, {21, 76}, {23, 78}, {18, 73}, {19, 72}, {22, 77}, {23, 76}, {20, 73}, {22, 75}, {20, 75}, {21, 74}, {36, 64}, {53, 81}, {52, 80}, {47, 75}, {46, 74}, {45, 73}, {44, 72}, {39, 67}, {38, 66}, {37, 65}, {38, 64}, {54, 80}, {47, 73}, {46, 72}, {39, 65}, {40, 66}, {45, 71}, {44, 70}, {41, 67}, {40, 68}, {43, 71}, {42, 70}, {41, 69}, {42, 68}, {43, 69}, {48, 74}, {53, 79}, {52, 78}, {49, 75}, {48, 76}, {51, 79}, {50, 78}, {49, 77}, {50, 76}, {51, 77} }>;

(II) A more general form is to represent the graph as the orbit of {54, 55} under the group generated by the following permutations:

a: (28, 55)(29, 56)(30, 57)(31, 58)(32, 59)(33, 60)(34, 61)(35, 62)(36, 63)(37, 64)(38, 65)(39, 66)(40, 67)(41, 68)(42, 69)(43, 70)(44, 71)(45, 72)(46, 73)(47, 74)(48, 75)(49, 76)(50, 77)(51, 78)(52, 79)(53, 80)(54, 81)
b: (2, 27)(3, 26)(4, 25)(5, 24)(6, 23)(7, 22)(8, 21)(9, 20)(10, 19)(11, 18)(12, 17)(13, 16)(14, 15)(29, 54)(30, 53)(31, 52)(32, 51)(33, 50)(34, 49)(35, 48)(36, 47)(37, 46)(38, 45)(39, 44)(40, 43)(41, 42)(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)
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)
d: (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)

(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[ 81, 1 ]
81
-1 56 81 29 54
-2 55 57 28 30
-3 56 58 29 31
-4 57 59 30 32
-5 33 58 60 31
-6 34 59 61 32
-7 33 35 60 62
-8 34 36 61 63
-9 35 37 62 64
-10 36 38 63 65
-11 66 37 39 64
-12 67 38 40 65
-13 66 68 39 41
-14 67 69 40 42
-15 68 70 41 43
-16 44 69 71 42
-17 45 70 72 43
-18 44 46 71 73
-19 45 47 72 74
-20 46 48 73 75
-21 47 49 74 76
-22 77 48 50 75
-23 78 49 51 76
-24 77 79 50 52
-25 78 80 51 53
-26 79 81 52 54
-27 55 80 28 53
-28 56 2 81 27
-29 55 1 57 3
-30 56 2 58 4
-31 57 3 59 5
-32 58 4 60 6
-33 59 5 61 7
-34 60 6 62 8
-35 61 7 63 9
-36 62 8 64 10
-37 11 63 9 65
-38 66 12 64 10
-39 11 67 13 65
-40 66 12 68 14
-41 67 13 69 15
-42 68 14 70 16
-43 69 15 71 17
-44 70 16 72 18
-45 71 17 73 19
-46 72 18 74 20
-47 73 19 75 21
-48 22 74 20 76
-49 77 23 75 21
-50 22 78 24 76
-51 77 23 79 25
-52 78 24 80 26
-53 79 25 81 27
-54 55 1 80 26
-55 2 27 29 54
-56 1 3 28 30
-57 2 4 29 31
-58 3 5 30 32
-59 33 4 6 31
-60 34 5 7 32
-61 33 35 6 8
-62 34 36 7 9
-63 35 37 8 10
-64 11 36 38 9
-65 12 37 39 10
-66 11 13 38 40
-67 12 14 39 41
-68 13 15 40 42
-69 14 16 41 43
-70 44 15 17 42
-71 45 16 18 43
-72 44 46 17 19
-73 45 47 18 20
-74 46 48 19 21
-75 22 47 49 20
-76 23 48 50 21
-77 22 24 49 51
-78 23 25 50 52
-79 24 26 51 53
-80 25 27 52 54
-81 1 26 28 53
0

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