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On this page are computer-accessible forms for the graph C4[ 54, 4 ] = MC3(6,9,1,6,2,0,1).

(I) Following is a form readable by MAGMA:

g:=Graph<54|{ {2, 11}, {20, 29}, {18, 27}, {16, 25}, {4, 13}, {6, 15}, {22, 31}, {32, 41}, {34, 43}, {36, 45}, {38, 47}, {1, 10}, {17, 26}, {5, 14}, {21, 30}, {33, 42}, {37, 46}, {3, 12}, {19, 28}, {35, 44}, {9, 28}, {7, 16}, {15, 24}, {39, 48}, {4, 28}, {5, 29}, {6, 30}, {7, 31}, {8, 17}, {44, 53}, {10, 19}, {12, 21}, {14, 23}, {40, 49}, {42, 51}, {9, 18}, {45, 54}, {13, 22}, {41, 50}, {1, 29}, {2, 30}, {3, 31}, {11, 20}, {43, 52}, {2, 35}, {20, 53}, {19, 50}, {21, 52}, {23, 54}, {10, 40}, {15, 45}, {11, 41}, {14, 44}, {1, 34}, {15, 44}, {11, 40}, {21, 54}, {22, 53}, {4, 32}, {5, 33}, {6, 34}, {7, 35}, {12, 41}, {14, 43}, {12, 42}, {13, 43}, {3, 36}, {20, 51}, {19, 52}, {13, 42}, {8, 32}, {9, 33}, {24, 48}, {25, 49}, {26, 50}, {27, 51}, {26, 48}, {27, 49}, {8, 36}, {2, 47}, {10, 39}, {1, 46}, {3, 48}, {7, 52}, {17, 37}, {18, 38}, {4, 49}, {18, 39}, {16, 37}, {6, 51}, {24, 46}, {25, 47}, {5, 50}, {17, 38}, {23, 32}, {31, 40}, {22, 46}, {23, 47}, {24, 33}, {26, 35}, {28, 37}, {30, 39}, {25, 34}, {29, 38}, {8, 53}, {16, 45}, {9, 54}, {27, 36} }>;

(II) A more general form is to represent the graph as the orbit of {2, 11} under the group generated by the following permutations:

a: (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, 43, 44, 45)(46, 47, 48, 49, 50, 51, 52, 53, 54)
b: (2, 44, 7, 26)(3, 41, 23, 45)(4, 9, 27, 42)(5, 25, 24, 40)(6, 22, 19, 38)(8, 21)(10, 29, 34, 46)(11, 14, 16, 48)(12, 32, 54, 36)(13, 28, 18, 51)(15, 31, 50, 47)(17, 30, 53, 52)(20, 43, 37, 39)(33, 49)
c: (1, 10, 39, 30, 21, 54, 23, 32, 8, 53, 22, 46)(2, 12, 45, 14, 4, 17, 20, 31, 24, 34, 19, 18)(3, 15, 43, 28, 38, 11)(5, 49, 26, 51, 7, 33, 25, 50, 27, 35, 42, 16)(6, 52, 9, 47, 41, 36, 44, 13, 37, 29, 40, 48)
d: (3, 8)(4, 42)(5, 19)(6, 25)(7, 44)(10, 29)(12, 32)(14, 52)(15, 16)(17, 48)(20, 40)(21, 23)(24, 37)(28, 33)(30, 47)(31, 53)(38, 39)(49, 51)

(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.

**************

&Graph
C4[ 54, 4 ]
54
-1 34 46 29 10
-2 11 35 47 30
-3 12 36 48 31
-4 13 49 28 32
-5 33 14 50 29
-6 34 15 51 30
-7 35 16 52 31
-8 36 17 53 32
-9 33 28 18 54
-10 1 39 40 19
-11 2 40 41 20
-12 3 41 42 21
-13 22 4 42 43
-14 44 23 5 43
-15 44 45 24 6
-16 45 25 37 7
-17 26 37 38 8
-18 27 38 39 9
-19 28 50 52 10
-20 11 29 51 53
-21 12 30 52 54
-22 13 46 31 53
-23 14 47 32 54
-24 33 46 15 48
-25 34 47 16 49
-26 35 48 17 50
-27 36 49 18 51
-28 4 37 19 9
-29 1 5 38 20
-30 2 6 39 21
-31 22 3 7 40
-32 23 4 8 41
-33 24 5 9 42
-34 1 25 6 43
-35 44 2 26 7
-36 45 3 27 8
-37 46 16 17 28
-38 47 17 18 29
-39 48 18 30 10
-40 11 49 31 10
-41 11 12 50 32
-42 33 12 13 51
-43 34 13 14 52
-44 35 14 15 53
-45 36 15 16 54
-46 22 1 24 37
-47 23 2 25 38
-48 24 3 26 39
-49 25 4 27 40
-50 26 5 19 41
-51 27 6 20 42
-52 7 19 21 43
-53 22 44 8 20
-54 23 45 9 21
0

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