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On this page are computer-accessible forms for the graph C4[ 68, 3 ] = PS(4,17;2).

(I) Following is a form readable by MAGMA:

g:=Graph<68|{ {33, 35}, {17, 18}, {48, 52}, {51, 55}, {50, 54}, {49, 53}, {34, 36}, {48, 61}, {50, 63}, {32, 47}, {49, 62}, {2, 18}, {12, 28}, {11, 27}, {10, 26}, {9, 25}, {8, 24}, {7, 23}, {6, 22}, {5, 21}, {4, 20}, {3, 19}, {13, 29}, {14, 30}, {15, 31}, {33, 48}, {1, 19}, {12, 30}, {9, 27}, {8, 26}, {5, 23}, {4, 22}, {13, 31}, {32, 51}, {47, 60}, {43, 56}, {39, 52}, {34, 49}, {40, 61}, {46, 59}, {44, 57}, {42, 63}, {2, 20}, {11, 29}, {10, 28}, {3, 21}, {41, 62}, {45, 58}, {35, 56}, {39, 60}, {36, 57}, {42, 55}, {40, 53}, {38, 59}, {6, 24}, {7, 25}, {37, 58}, {41, 54}, {18, 50}, {19, 51}, {1, 34}, {16, 58}, {17, 59}, {16, 59}, {17, 60}, {31, 50}, {29, 48}, {14, 32}, {15, 33}, {30, 49}, {16, 32}, {17, 33}, {21, 36}, {31, 46}, {29, 44}, {27, 42}, {23, 38}, {25, 40}, {16, 34}, {20, 39}, {30, 45}, {28, 47}, {22, 37}, {24, 43}, {26, 41}, {13, 56}, {27, 46}, {15, 58}, {19, 38}, {25, 44}, {14, 56}, {15, 57}, {14, 57}, {28, 43}, {26, 45}, {18, 37}, {20, 35}, {12, 54}, {13, 55}, {4, 63}, {12, 55}, {1, 61}, {3, 63}, {2, 62}, {1, 60}, {11, 54}, {9, 52}, {3, 62}, {21, 40}, {23, 42}, {10, 52}, {11, 53}, {2, 61}, {10, 53}, {22, 41}, {24, 39}, {4, 64}, {7, 67}, {6, 66}, {5, 65}, {5, 64}, {7, 66}, {6, 65}, {8, 67}, {8, 68}, {9, 68}, {35, 65}, {38, 68}, {36, 66}, {37, 67}, {43, 64}, {47, 68}, {44, 65}, {46, 67}, {45, 66}, {51, 64} }>;

(II) A more general form is to represent the graph as the orbit of {33, 35} under the group generated by the following permutations:

a: (1, 18, 35, 52)(2, 33, 39, 61, 17, 20, 48, 60)(3, 31, 43, 53, 16, 22, 44, 68)(4, 29, 47, 62, 15, 24, 40, 59)(5, 27, 51, 54, 14, 26, 36, 67)(6, 25, 38, 63, 13, 28, 49, 58)(7, 23, 42, 55, 12, 30, 45, 66)(8, 21, 46, 64, 11, 32, 41, 57)(9, 19, 50, 56, 10, 34, 37, 65)
b: (2, 17)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(19, 34)(20, 33)(21, 32)(22, 31)(23, 30)(24, 29)(25, 28)(26, 27)(36, 51)(37, 50)(38, 49)(39, 48)(40, 47)(41, 46)(42, 45)(43, 44)(53, 68)(54, 67)(55, 66)(56, 65)(57, 64)(58, 63)(59, 62)(60, 61)
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, 64, 65, 66, 67, 68)

(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[ 68, 3 ]
68
-1 34 60 61 19
-2 61 18 62 20
-3 62 19 63 21
-4 22 63 20 64
-5 23 64 21 65
-6 22 66 24 65
-7 66 23 67 25
-8 67 24 68 26
-9 68 25 27 52
-10 26 28 52 53
-11 27 29 53 54
-12 55 28 30 54
-13 55 56 29 31
-14 56 57 30 32
-15 33 57 58 31
-16 34 58 59 32
-17 33 59 60 18
-18 2 37 17 50
-19 1 3 38 51
-20 2 35 4 39
-21 3 36 5 40
-22 4 37 6 41
-23 5 38 7 42
-24 6 39 8 43
-25 44 7 40 9
-26 45 8 41 10
-27 11 46 9 42
-28 12 47 10 43
-29 11 44 13 48
-30 12 45 14 49
-31 13 46 15 50
-32 14 47 16 51
-33 35 15 48 17
-34 1 36 16 49
-35 33 56 20 65
-36 66 34 57 21
-37 22 67 58 18
-38 23 68 59 19
-39 24 60 52 20
-40 25 61 53 21
-41 22 26 62 54
-42 55 23 27 63
-43 56 24 28 64
-44 57 25 29 65
-45 66 58 26 30
-46 67 59 27 31
-47 68 60 28 32
-48 33 61 29 52
-49 34 62 30 53
-50 18 63 31 54
-51 55 19 64 32
-52 48 39 9 10
-53 11 49 40 10
-54 11 12 50 41
-55 12 13 51 42
-56 13 35 14 43
-57 44 14 36 15
-58 45 15 37 16
-59 46 16 38 17
-60 1 47 17 39
-61 1 2 48 40
-62 2 3 49 41
-63 3 4 50 42
-64 4 5 51 43
-65 44 35 5 6
-66 45 36 6 7
-67 46 37 7 8
-68 47 38 8 9
0

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