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On this page are computer-accessible forms for the graph C4[ 32, 4 ] = MPS(4,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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