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On this page are computer-accessible forms for the graph C4[ 40, 6 ] = MPS(4,20;3).

(I) Following is a form readable by MAGMA:

g:=Graph<40|{ {20, 22}, {27, 31}, {26, 31}, {19, 21}, {2, 11}, {20, 29}, {18, 27}, {6, 15}, {4, 13}, {16, 25}, {1, 11}, {5, 15}, {4, 14}, {5, 14}, {17, 26}, {16, 28}, {18, 30}, {17, 29}, {2, 12}, {3, 13}, {3, 12}, {19, 28}, {12, 24}, {13, 25}, {14, 26}, {15, 27}, {1, 20}, {10, 31}, {11, 30}, {6, 16}, {7, 17}, {7, 16}, {15, 24}, {8, 17}, {10, 19}, {12, 21}, {14, 23}, {8, 18}, {9, 19}, {9, 18}, {13, 22}, {3, 31}, {11, 23}, {10, 20}, {1, 32}, {9, 40}, {7, 38}, {5, 36}, {3, 34}, {2, 33}, {6, 37}, {4, 32}, {7, 35}, {6, 34}, {5, 33}, {1, 39}, {4, 35}, {2, 40}, {8, 36}, {9, 37}, {10, 38}, {8, 39}, {21, 36}, {25, 40}, {23, 38}, {22, 36}, {26, 40}, {23, 37}, {22, 37}, {21, 35}, {27, 32}, {28, 32}, {30, 34}, {29, 33}, {28, 33}, {30, 35}, {24, 38}, {25, 39}, {24, 39}, {29, 34} }>;

(II) A more general form is to represent the graph as the orbit of {20, 22} under the group generated by the following permutations:

a: (2, 4, 10, 8)(3, 7, 9, 5)(11, 32, 20, 39)(12, 35, 19, 36)(13, 38, 18, 33)(14, 31, 17, 40)(15, 34, 16, 37)(22, 24, 30, 28)(23, 27, 29, 25)
b: (2, 10)(3, 9)(4, 8)(5, 7)(11, 20)(12, 19)(13, 18)(14, 17)(15, 16)(22, 30)(23, 29)(24, 28)(25, 27)(31, 40)(32, 39)(33, 38)(34, 37)(35, 36)
c: (1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 10, 20)(21, 31, 22, 32, 23, 33, 24, 34, 25, 35, 26, 36, 27, 37, 28, 38, 29, 39, 30, 40)
d: (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)

(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[ 40, 6 ]
40
-1 11 39 20 32
-2 11 33 12 40
-3 12 34 13 31
-4 13 35 14 32
-5 33 14 36 15
-6 34 15 37 16
-7 35 16 38 17
-8 36 17 39 18
-9 37 18 40 19
-10 38 19 20 31
-11 1 23 2 30
-12 2 24 3 21
-13 22 3 25 4
-14 23 4 26 5
-15 24 5 27 6
-16 25 6 28 7
-17 26 7 29 8
-18 27 8 30 9
-19 28 9 10 21
-20 22 1 29 10
-21 12 35 36 19
-22 13 36 37 20
-23 11 14 37 38
-24 12 15 38 39
-25 13 16 39 40
-26 14 17 40 31
-27 15 18 31 32
-28 33 16 19 32
-29 33 34 17 20
-30 11 34 35 18
-31 3 26 27 10
-32 1 4 27 28
-33 2 5 28 29
-34 3 6 29 30
-35 4 7 30 21
-36 22 5 8 21
-37 22 23 6 9
-38 23 24 7 10
-39 1 24 25 8
-40 2 25 26 9
0

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