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On this page are computer-accessible forms for the graph C4[ 40, 9 ] = PL(MBr(2, 10; 3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {17, 21} under the group generated by the following permutations:

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

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