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On this page are computer-accessible forms for the graph C4[ 54, 5 ] = AMC(6,3,[0.1:2.2]).

(I) Following is a form readable by MAGMA:

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

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

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

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