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On this page are computer-accessible forms for the graph C4[ 27, 3 ] = AMC(3,3,[0.1:2.2]).

(I) Following is a form readable by MAGMA:

g:=Graph<27|{ {8, 11}, {9, 12}, {8, 14}, {9, 15}, {17, 25}, {18, 26}, {6, 12}, {17, 27}, {16, 26}, {7, 13}, {16, 27}, {18, 25}, {1, 13}, {3, 15}, {2, 14}, {7, 10}, {4, 10}, {5, 11}, {1, 16}, {4, 21}, {3, 18}, {6, 20}, {2, 17}, {7, 20}, {4, 16}, {6, 18}, {5, 17}, {3, 22}, {13, 24}, {1, 23}, {14, 24}, {5, 19}, {11, 19}, {15, 23}, {12, 20}, {14, 22}, {3, 26}, {15, 22}, {1, 27}, {2, 24}, {9, 19}, {13, 23}, {2, 25}, {8, 21}, {4, 26}, {5, 27}, {8, 22}, {9, 23}, {10, 20}, {11, 21}, {6, 25}, {7, 24}, {10, 21}, {12, 19} }>;

(II) A more general form is to represent the graph as the orbit of {8, 11} under the group generated by the following permutations:

a: (2, 3)(4, 7)(5, 9)(6, 8)(11, 12)(13, 16)(14, 18)(15, 17)(20, 21)(22, 25)(23, 27)(24, 26)
b: (1, 2)(4, 8)(5, 7)(6, 9)(10, 11)(13, 17)(14, 16)(15, 18)(19, 20)(22, 26)(23, 25)(24, 27)
c: (2, 10, 3, 19)(4, 15, 5, 24)(7, 26, 9, 17)(11, 14, 21, 22)(12, 25, 20, 18)(13, 16, 23, 27)

(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[ 27, 3 ]
27
-1 23 13 16 27
-2 24 14 25 17
-3 22 15 26 18
-4 26 16 10 21
-5 11 27 17 19
-6 12 25 18 20
-7 13 24 20 10
-8 11 22 14 21
-9 12 23 15 19
-10 4 7 20 21
-11 5 8 19 21
-12 6 19 9 20
-13 1 23 24 7
-14 22 2 24 8
-15 22 23 3 9
-16 1 4 26 27
-17 2 25 5 27
-18 3 25 26 6
-19 11 12 5 9
-20 12 6 7 10
-21 11 4 8 10
-22 3 14 15 8
-23 1 13 15 9
-24 2 13 14 7
-25 2 6 17 18
-26 3 4 16 18
-27 1 5 16 17
0

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