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On this page are computer-accessible forms for the graph C4[ 40, 7 ] = R_20(12,11).

(I) Following is a form readable by MAGMA:

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

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

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

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