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

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

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

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

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