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On this page are computer-accessible forms for the graph C4[ 64, 1 ] = W(32,2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

a: (21, 53)
b: (20, 52)
c: (22, 54)
d: (13, 45)
e: (4, 36)
f: (2, 34)
g: (30, 62)
h: (2, 32)(3, 31)(4, 30)(5, 29)(6, 28)(7, 27)(8, 26)(9, 25)(10, 24)(11, 23)(12, 22)(13, 21)(14, 20)(15, 19)(16, 18)(34, 64)(35, 63)(36, 62)(37, 61)(38, 60)(39, 59)(40, 58)(41, 57)(42, 56)(43, 55)(44, 54)(45, 53)(46, 52)(47, 51)(48, 50)
m: (28, 60)
n1: (8, 40)
a1: (14, 46)
b1: (11, 43)
c1: (32, 64)
d1: (27, 59)
e1: (18, 50)
f1: (5, 37)
g1: (10, 42)
h1: (12, 44)
m1: (7, 39)
n2: (19, 51)
a2: (25, 57)
b2: (29, 61)
c2: (3, 35)
d2: (9, 41)
e2: (26, 58)
f2: (6, 38)
g2: (16, 48)
h2: (17, 49)
m2: (24, 56)
n3: (31, 63)
a3: (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)
b3: (23, 55)

(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.

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&Graph
C4[ 64, 1 ]
64
-1 34 2 64 32
-2 33 1 35 3
-3 34 2 36 4
-4 35 3 37 5
-5 36 4 38 6
-6 37 5 39 7
-7 38 6 40 8
-8 39 7 41 9
-9 40 8 42 10
-10 11 41 9 43
-11 44 12 42 10
-12 11 45 13 43
-13 44 12 46 14
-14 45 13 47 15
-15 46 14 48 16
-16 47 15 49 17
-17 48 16 50 18
-18 49 17 51 19
-19 50 18 52 20
-20 51 19 53 21
-21 22 52 20 54
-22 55 23 53 21
-23 22 56 24 54
-24 55 23 57 25
-25 56 24 58 26
-26 57 25 59 27
-27 58 26 60 28
-28 59 27 61 29
-29 60 28 62 30
-30 61 29 63 31
-31 62 30 64 32
-32 33 1 63 31
-33 34 2 64 32
-34 33 1 35 3
-35 34 2 36 4
-36 35 3 37 5
-37 36 4 38 6
-38 37 5 39 7
-39 38 6 40 8
-40 39 7 41 9
-41 40 8 42 10
-42 11 41 9 43
-43 44 12 42 10
-44 11 45 13 43
-45 44 12 46 14
-46 45 13 47 15
-47 46 14 48 16
-48 47 15 49 17
-49 48 16 50 18
-50 49 17 51 19
-51 50 18 52 20
-52 51 19 53 21
-53 22 52 20 54
-54 55 23 53 21
-55 22 56 24 54
-56 55 23 57 25
-57 56 24 58 26
-58 57 25 59 27
-59 58 26 60 28
-60 59 27 61 29
-61 60 28 62 30
-62 61 29 63 31
-63 62 30 64 32
-64 33 1 63 31
0

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