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On this page are computer-accessible forms for the graph C4[ 64, 6 ] = MPS(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}, {7, 15}, {6, 14}, {5, 13}, {4, 12}, {3, 11}, {2, 10}, {33, 41}, {34, 42}, {35, 43}, {3, 10}, {39, 46}, {37, 44}, {7, 14}, {5, 12}, {35, 42}, {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}, {18, 29}, {22, 25}, {36, 43}, {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, 57}, {26, 40}, {20, 32}, {21, 32}, {29, 40}, {8, 62}, {2, 59}, {6, 63}, {4, 61}, {3, 57}, {7, 61}, {6, 60}, {27, 33}, {30, 36}, {31, 37}, {1, 58}, {5, 62}, {28, 39}, {25, 36}, {27, 38}, {31, 34}, {1, 63}, {5, 59}, {4, 58}, {25, 39}, {28, 34}, {29, 35}, {3, 60}, {26, 37}, {30, 33}, {2, 64}, {7, 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, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15, 8, 16)(17, 57, 18, 58, 19, 59, 20, 60, 21, 61, 22, 62, 23, 63, 24, 64)(25, 50, 26, 51, 27, 52, 28, 53, 29, 54, 30, 55, 31, 56, 32, 49)(33, 45, 34, 46, 35, 47, 36, 48, 37, 41, 38, 42, 39, 43, 40, 44)
b: (2, 23, 4, 51)(3, 37, 7, 33)(6, 19, 8, 55)(9, 16, 58, 63)(10, 26, 61, 41)(11, 44, 64, 27)(12, 62, 59, 13)(14, 30, 57, 45)(15, 48, 60, 31)(17, 40, 49, 34)(18, 54, 52, 24)(20, 22, 50, 56)(21, 36, 53, 38)(25, 43, 46, 32)(28, 29, 47, 42)(35, 39)
c: (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)
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, 6 ]
64
-1 58 16 63 9
-2 59 9 64 10
-3 11 57 60 10
-4 11 12 58 61
-5 12 13 59 62
-6 13 14 60 63
-7 14 15 61 64
-8 57 15 16 62
-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 3 8 53 54
-58 55 1 4 54
-59 55 56 2 5
-60 56 3 49 6
-61 4 49 50 7
-62 5 50 51 8
-63 1 6 51 52
-64 2 7 52 53
0

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