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On this page are computer-accessible forms for the graph C4[ 42, 4 ] = MC3(6,7,1,3,3,0,1).

(I) Following is a form readable by MAGMA:

g:=Graph<42|{ {8, 15}, {32, 39}, {24, 31}, {16, 23}, {1, 8}, {35, 42}, {33, 40}, {23, 30}, {21, 28}, {19, 26}, {7, 14}, {5, 12}, {3, 10}, {17, 24}, {2, 9}, {34, 41}, {22, 29}, {18, 25}, {6, 13}, {4, 11}, {20, 27}, {13, 29}, {14, 30}, {6, 23}, {7, 22}, {12, 29}, {14, 31}, {5, 22}, {13, 30}, {1, 23}, {8, 31}, {1, 25}, {4, 28}, {3, 27}, {2, 26}, {9, 16}, {11, 18}, {13, 20}, {15, 22}, {2, 24}, {6, 28}, {3, 25}, {10, 17}, {14, 21}, {4, 26}, {5, 27}, {7, 24}, {12, 19}, {4, 39}, {1, 36}, {3, 38}, {15, 42}, {2, 37}, {8, 32}, {10, 34}, {9, 33}, {11, 35}, {9, 32}, {11, 34}, {15, 38}, {10, 33}, {5, 40}, {7, 42}, {6, 41}, {12, 35}, {20, 36}, {21, 37}, {16, 36}, {19, 39}, {18, 38}, {17, 37}, {16, 39}, {17, 40}, {31, 38}, {29, 36}, {27, 34}, {25, 32}, {19, 42}, {18, 41}, {30, 37}, {26, 33}, {20, 40}, {21, 41}, {28, 35} }>;

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

a: (1, 8)(2, 41)(3, 39)(4, 10)(5, 12)(6, 24)(7, 13)(9, 18)(11, 33)(14, 30)(15, 36)(16, 38)(17, 28)(19, 27)(20, 42)(21, 37)(22, 29)(23, 31)(25, 32)(26, 34)(35, 40)
b: (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, 41, 42)
c: (2, 19)(3, 18)(4, 33)(5, 21)(6, 20)(9, 39)(10, 11)(12, 37)(14, 22)(15, 31)(17, 35)(23, 36)(24, 42)(27, 41)(28, 40)(29, 30)
d: (2, 4, 33, 19)(3, 29, 31, 6)(5, 7, 21, 34)(8, 23, 25, 36)(9, 39)(10, 12, 24, 28)(11, 40, 42, 37)(13, 38)(14, 41, 27, 22)(15, 30, 18, 20)(16, 32)(17, 35)

(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[ 42, 4 ]
42
-1 23 25 36 8
-2 24 26 37 9
-3 25 27 38 10
-4 11 26 28 39
-5 22 12 27 40
-6 23 13 28 41
-7 22 24 14 42
-8 1 15 31 32
-9 33 2 16 32
-10 33 34 3 17
-11 34 35 4 18
-12 35 5 29 19
-13 6 29 30 20
-14 7 30 31 21
-15 22 38 8 42
-16 23 36 39 9
-17 24 37 40 10
-18 11 25 38 41
-19 12 26 39 42
-20 13 36 27 40
-21 14 37 28 41
-22 15 5 7 29
-23 1 16 6 30
-24 2 17 7 31
-25 1 3 18 32
-26 33 2 4 19
-27 34 3 5 20
-28 35 4 6 21
-29 22 12 13 36
-30 23 13 14 37
-31 24 14 38 8
-32 25 39 8 9
-33 26 40 9 10
-34 11 27 41 10
-35 11 12 28 42
-36 1 16 29 20
-37 2 17 30 21
-38 3 15 18 31
-39 4 16 19 32
-40 33 5 17 20
-41 34 6 18 21
-42 35 15 7 19
0

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