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On this page are computer-accessible forms for the graph C4[ 57, 2 ] = PS(3,19;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {19, 20} 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, 55, 56, 57)
b: (2, 19)(3, 18)(4, 17)(5, 16)(6, 15)(7, 14)(8, 13)(9, 12)(10, 11)(21, 38)(22, 37)(23, 36)(24, 35)(25, 34)(26, 33)(27, 32)(28, 31)(29, 30)(40, 57)(41, 56)(42, 55)(43, 54)(44, 53)(45, 52)(46, 51)(47, 50)(48, 49)
c: (1, 20, 39)(2, 32, 50, 19, 27, 47)(3, 25, 42, 18, 34, 55)(4, 37, 53, 17, 22, 44)(5, 30, 45, 16, 29, 52)(6, 23, 56, 15, 36, 41)(7, 35, 48, 14, 24, 49)(8, 28, 40, 13, 31, 57)(9, 21, 51, 12, 38, 46)(10, 33, 43, 11, 26, 54)

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

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