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On this page are computer-accessible forms for the graph C4[ 63, 4 ] = PS(3,21;4).

(I) Following is a form readable by MAGMA:

g:=Graph<63|{ {21, 22}, {40, 44}, {42, 46}, {41, 45}, {39, 43}, {32, 49}, {42, 59}, {40, 57}, {38, 55}, {36, 53}, {34, 51}, {33, 50}, {41, 58}, {37, 54}, {2, 22}, {3, 23}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {1, 23}, {8, 30}, {9, 31}, {35, 52}, {32, 57}, {38, 63}, {36, 61}, {34, 59}, {2, 24}, {3, 25}, {6, 28}, {7, 29}, {33, 58}, {37, 62}, {4, 24}, {5, 25}, {6, 26}, {7, 27}, {4, 26}, {5, 27}, {35, 60}, {39, 56}, {8, 45}, {16, 53}, {10, 47}, {18, 55}, {24, 62}, {25, 63}, {9, 46}, {31, 56}, {17, 54}, {23, 48}, {24, 49}, {26, 51}, {28, 53}, {30, 55}, {10, 32}, {15, 37}, {14, 36}, {11, 33}, {22, 60}, {23, 61}, {1, 42}, {7, 44}, {19, 56}, {25, 50}, {29, 54}, {12, 32}, {15, 35}, {14, 34}, {13, 33}, {6, 43}, {20, 57}, {12, 34}, {13, 35}, {16, 63}, {31, 48}, {21, 58}, {27, 52}, {1, 48}, {15, 62}, {13, 60}, {11, 58}, {3, 50}, {5, 52}, {7, 54}, {9, 56}, {26, 43}, {28, 45}, {30, 47}, {2, 49}, {14, 61}, {6, 53}, {10, 57}, {29, 46}, {16, 36}, {17, 37}, {18, 38}, {19, 39}, {16, 38}, {17, 39}, {4, 51}, {12, 59}, {27, 44}, {22, 47}, {1, 59}, {4, 62}, {5, 63}, {17, 43}, {18, 40}, {19, 41}, {20, 46}, {21, 47}, {11, 48}, {15, 52}, {20, 40}, {21, 41}, {12, 49}, {14, 51}, {2, 60}, {3, 61}, {18, 44}, {19, 45}, {20, 42}, {8, 55}, {13, 50} }>;

(II) A more general form is to represent the graph as the orbit of {21, 22} under the group generated by the following permutations:

a: (1, 22, 43)(2, 39, 59, 21, 26, 48)(3, 35, 54, 20, 30, 53)(4, 31, 49, 19, 34, 58)(5, 27, 44, 18, 38, 63)(6, 23, 60, 17, 42, 47)(7, 40, 55, 16, 25, 52)(8, 36, 50, 15, 29, 57)(9, 32, 45, 14, 33, 62)(10, 28, 61, 13, 37, 46)(11, 24, 56, 12, 41, 51)
b: (2, 21)(3, 20)(4, 19)(5, 18)(6, 17)(7, 16)(8, 15)(9, 14)(10, 13)(11, 12)(23, 42)(24, 41)(25, 40)(26, 39)(27, 38)(28, 37)(29, 36)(30, 35)(31, 34)(32, 33)(44, 63)(45, 62)(46, 61)(47, 60)(48, 59)(49, 58)(50, 57)(51, 56)(52, 55)(53, 54)
c: (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, 55, 56, 57, 58, 59, 60, 61, 62, 63)

(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[ 63, 4 ]
63
-1 23 48 59 42
-2 22 24 49 60
-3 23 25 50 61
-4 24 26 51 62
-5 25 27 52 63
-6 26 28 53 43
-7 44 27 29 54
-8 55 45 28 30
-9 56 46 29 31
-10 57 47 30 32
-11 33 58 48 31
-12 34 59 49 32
-13 33 35 60 50
-14 34 36 61 51
-15 35 37 62 52
-16 36 38 63 53
-17 37 39 43 54
-18 44 55 38 40
-19 45 56 39 41
-20 46 57 40 42
-21 22 47 58 41
-22 2 47 60 21
-23 1 3 48 61
-24 2 4 49 62
-25 3 5 50 63
-26 4 6 51 43
-27 44 5 7 52
-28 45 6 8 53
-29 46 7 9 54
-30 55 47 8 10
-31 11 56 48 9
-32 12 57 49 10
-33 11 13 58 50
-34 12 14 59 51
-35 13 15 60 52
-36 14 16 61 53
-37 15 17 62 54
-38 55 16 18 63
-39 56 17 19 43
-40 44 57 18 20
-41 45 58 19 21
-42 1 46 59 20
-43 26 6 17 39
-44 27 7 18 40
-45 28 8 19 41
-46 29 9 20 42
-47 22 30 10 21
-48 11 1 23 31
-49 12 2 24 32
-50 33 13 3 25
-51 34 14 4 26
-52 35 15 5 27
-53 36 16 6 28
-54 37 17 7 29
-55 38 18 8 30
-56 39 19 9 31
-57 40 20 10 32
-58 11 33 41 21
-59 1 12 34 42
-60 22 2 13 35
-61 23 3 14 36
-62 24 4 15 37
-63 25 5 16 38
0

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