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On this page are computer-accessible forms for the graph C4[ 64, 5 ] = PS(8,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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