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On this page are computer-accessible forms for the graph C4[ 64, 13 ] = KE_16(1,7,2,11,1).

(I) Following is a form readable by MAGMA:

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

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

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