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On this page are computer-accessible forms for the graph C4[ 40, 5 ] = PS(8,5;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {9, 11} under the group generated by the following permutations:

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

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