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

On this page are computer-accessible forms for the graph C4[ 64, 16 ] = SDD({4,4}_4,0).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 36} under the group generated by the following permutations:

a: (6, 22)
b: (5, 32)
c: (3, 29)
d: (2, 6)(5, 10)(7, 8)(11, 31)(15, 32)(17, 18)(19, 20)(22, 23)(33, 37)(36, 49)(38, 44)(39, 42)(40, 43)(41, 54)(45, 61)(48, 60)(51, 53)(52, 55)(57, 58)(63, 64)
e: (1, 2, 9, 6)(3, 5, 14, 10)(4, 7, 12, 8)(11, 26, 31, 16)(13, 18, 24, 17)(15, 29, 32, 21)(19, 27, 20, 25)(22, 30, 23, 28)(33, 41, 54, 37)(34, 36, 56, 49)(35, 38, 50, 44)(39, 48, 60, 42)(40, 43, 45, 61)(46, 53, 59, 51)(47, 52, 62, 55)(57, 58, 63, 64)
f: (18, 19)
g: (2, 4)(5, 13)(8, 9)(14, 17)(16, 23)(20, 21)(25, 32)(28, 31)(33, 35)(36, 47)(38, 43)(39, 46)(40, 41)(44, 54)(48, 57)(50, 61)(51, 60)(53, 58)(55, 56)(59, 64)
h: (3, 4)(5, 7)(8, 10)(11, 32)(12, 14)(15, 31)(16, 29)(21, 26)(34, 35)(36, 38)(39, 43)(40, 42)(44, 49)(45, 48)(46, 47)(50, 56)(51, 55)(52, 53)(59, 62)(60, 61)
m: (9, 28)
n1: (24, 27)
a1: (10, 15)
b1: (2, 23)
c1: (13, 25)
d1: (4, 16)
e1: (8, 31)
f1: (7, 11)

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

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