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On this page are computer-accessible forms for the graph C4[ 40, 6 ] = R_20(6, 1).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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