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On this page are computer-accessible forms for the graph C4[ 40, 8 ] = PX(5,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

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

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

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