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On this page are computer-accessible forms for the graph C4[ 27, 3 ] = L(F18).

(I) Following is a form readable by MAGMA:

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

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

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

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