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On this page are computer-accessible forms for the graph C4[ 64, 17 ] = SDD(W(8,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 58} under the group generated by the following permutations:

a: (9, 13)
b: (24, 26)(27, 28)(52, 54)(55, 57)(60, 63)(62, 64)
c: (7, 9)(10, 13)(38, 41)(42, 45)(48, 51)(50, 53)
d: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 15)(11, 17)(13, 19)(14, 21)(16, 22)(18, 25)(20, 23)(24, 29)(26, 30)(27, 31)(28, 32)(34, 36)(35, 38)(37, 41)(40, 42)(43, 48)(44, 45)(46, 50)(47, 51)(49, 53)(52, 56)(54, 58)(55, 59)(57, 61)(62, 63)
e: (3, 12)
f: (14, 20)
g: (11, 14)(16, 20)(43, 46)(47, 49)(52, 55)(54, 57)
h: (30, 32)
m: (21, 23)
n1: (5, 8)
a1: (29, 30)(31, 32)(56, 58)(59, 61)(60, 62)(63, 64)
b1: (4, 6)(15, 19)(35, 37)(40, 44)(43, 47)(46, 49)
c1: (2, 4)(3, 6)(7, 11)(9, 14)(10, 16)(12, 19)(13, 20)(15, 18)(17, 24)(21, 26)(22, 27)(23, 28)(33, 35)(34, 37)(36, 40)(38, 43)(39, 44)(41, 46)(42, 47)(45, 49)(48, 52)(50, 54)(51, 55)(53, 57)(56, 60)(58, 62)(59, 63)(61, 64)
d1: (6, 19)
e1: (17, 21)(22, 23)(48, 50)(51, 53)(56, 59)(58, 61)
f1: (2, 3)(12, 18)(33, 34)(36, 39)(38, 42)(41, 45)
g1: (26, 28)

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

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