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On this page are computer-accessible forms for the graph C4[ 66, 1 ] = W(33,2).

(I) Following is a form readable by MAGMA:

g:=Graph<66|{ {2, 3}, {64, 65}, {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}, {65, 66}, {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}, {1, 33}, {22, 54}, {21, 53}, {20, 52}, {19, 51}, {18, 50}, {17, 49}, {16, 48}, {15, 47}, {14, 46}, {2, 34}, {3, 35}, {4, 36}, {5, 37}, {6, 38}, {7, 39}, {8, 40}, {9, 41}, {10, 42}, {11, 43}, {12, 44}, {13, 45}, {23, 55}, {24, 56}, {25, 57}, {26, 58}, {27, 59}, {28, 60}, {29, 61}, {30, 62}, {31, 63}, {1, 35}, {21, 55}, {20, 54}, {17, 51}, {16, 50}, {4, 38}, {5, 39}, {8, 42}, {9, 43}, {12, 46}, {13, 47}, {24, 58}, {25, 59}, {28, 62}, {29, 63}, {2, 36}, {19, 53}, {18, 52}, {3, 37}, {10, 44}, {11, 45}, {26, 60}, {27, 61}, {6, 40}, {7, 41}, {22, 56}, {23, 57}, {14, 48}, {15, 49}, {31, 32}, {1, 66}, {30, 64}, {31, 65}, {32, 64}, {33, 65}, {34, 66}, {32, 66}, {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: (19, 52)
b: (17, 50)
c: (24, 57)
d: (4, 37)
e: (33, 66)
f: (2, 33)(3, 32)(4, 31)(5, 30)(6, 29)(7, 28)(8, 27)(9, 26)(10, 25)(11, 24)(12, 23)(13, 22)(14, 21)(15, 20)(16, 19)(17, 18)(35, 66)(36, 65)(37, 64)(38, 63)(39, 62)(40, 61)(41, 60)(42, 59)(43, 58)(44, 57)(45, 56)(46, 55)(47, 54)(48, 53)(49, 52)(50, 51)
g: (20, 53)
h: (8, 41)
m: (3, 36)
n1: (31, 64)
a1: (29, 62)
b1: (14, 47)
c1: (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)
d1: (18, 51)
e1: (32, 65)
f1: (23, 56)
g1: (21, 54)
h1: (5, 38)
m1: (9, 42)
n2: (7, 40)
a2: (11, 44)
b2: (22, 55)
c2: (26, 59)
d2: (12, 45)
e2: (6, 39)
f2: (27, 60)
g2: (28, 61)
h2: (25, 58)
m2: (13, 46)
n3: (15, 48)
a3: (30, 63)
b3: (2, 35)
c3: (10, 43)

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

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