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On this page are computer-accessible forms for the graph C4[ 78, 3 ] = PS(6,13;2).

(I) Following is a form readable by MAGMA:

g:=Graph<78|{ {25, 27}, {13, 14}, {64, 67}, {48, 53}, {65, 68}, {50, 55}, {26, 28}, {49, 54}, {48, 56}, {49, 57}, {50, 58}, {51, 59}, {52, 60}, {32, 41}, {34, 43}, {36, 45}, {38, 47}, {64, 74}, {65, 75}, {16, 27}, {33, 42}, {20, 31}, {37, 46}, {51, 56}, {2, 14}, {3, 15}, {36, 40}, {37, 41}, {38, 42}, {39, 43}, {17, 28}, {19, 30}, {52, 57}, {1, 15}, {16, 31}, {18, 29}, {35, 44}, {15, 30}, {32, 49}, {34, 51}, {2, 16}, {3, 17}, {6, 20}, {7, 21}, {10, 24}, {11, 25}, {40, 58}, {41, 59}, {44, 62}, {45, 63}, {14, 29}, {33, 50}, {4, 16}, {13, 25}, {5, 17}, {6, 18}, {7, 19}, {12, 24}, {40, 61}, {42, 63}, {4, 18}, {5, 19}, {12, 26}, {42, 60}, {43, 61}, {35, 52}, {39, 48}, {41, 62}, {45, 53}, {46, 54}, {47, 55}, {1, 26}, {8, 20}, {9, 21}, {10, 22}, {11, 23}, {8, 22}, {9, 23}, {14, 38}, {15, 39}, {27, 49}, {30, 52}, {28, 50}, {29, 51}, {31, 48}, {17, 32}, {30, 47}, {28, 45}, {23, 38}, {21, 36}, {19, 34}, {18, 33}, {29, 46}, {22, 37}, {21, 32}, {23, 34}, {20, 35}, {31, 40}, {27, 44}, {22, 33}, {24, 35}, {25, 36}, {24, 39}, {26, 37}, {7, 66}, {13, 72}, {1, 73}, {2, 74}, {3, 75}, {4, 76}, {5, 77}, {6, 78}, {1, 72}, {3, 74}, {5, 76}, {7, 78}, {8, 66}, {13, 71}, {9, 67}, {12, 70}, {2, 73}, {12, 71}, {6, 77}, {8, 67}, {9, 68}, {11, 70}, {10, 68}, {11, 69}, {4, 75}, {10, 69}, {43, 64}, {44, 65}, {46, 64}, {47, 65}, {53, 69}, {62, 78}, {54, 70}, {55, 71}, {56, 72}, {57, 73}, {58, 74}, {59, 75}, {60, 76}, {61, 77}, {62, 72}, {63, 73}, {53, 76}, {55, 78}, {56, 66}, {57, 67}, {60, 70}, {61, 71}, {54, 77}, {63, 66}, {58, 68}, {59, 69} }>;

(II) A more general form is to represent the graph as the orbit of {25, 27} under the group generated by the following permutations:

a: (2, 13)(3, 12)(4, 11)(5, 10)(6, 9)(7, 8)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(28, 39)(29, 38)(30, 37)(31, 36)(32, 35)(33, 34)(41, 52)(42, 51)(43, 50)(44, 49)(45, 48)(46, 47)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(67, 78)(68, 77)(69, 76)(70, 75)(71, 74)(72, 73)
b: (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, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78)
c: (1, 14, 27, 40, 53, 66)(2, 25, 31, 45, 56, 73, 13, 16, 36, 48, 63, 72)(3, 23, 35, 50, 59, 67, 12, 18, 32, 43, 60, 78)(4, 21, 39, 42, 62, 74, 11, 20, 28, 51, 57, 71)(5, 19, 30, 47, 65, 68, 10, 22, 37, 46, 54, 77)(6, 17, 34, 52, 55, 75, 9, 24, 33, 41, 64, 70)(7, 15, 38, 44, 58, 69, 8, 26, 29, 49, 61, 76)

(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[ 78, 3 ]
78
-1 15 26 72 73
-2 14 16 73 74
-3 15 17 74 75
-4 16 18 75 76
-5 77 17 19 76
-6 77 78 18 20
-7 66 78 19 21
-8 22 66 67 20
-9 23 67 68 21
-10 22 24 68 69
-11 23 25 69 70
-12 24 26 70 71
-13 14 25 71 72
-14 2 13 38 29
-15 1 3 39 30
-16 2 4 27 31
-17 3 5 28 32
-18 33 4 6 29
-19 34 5 7 30
-20 35 6 8 31
-21 36 7 9 32
-22 33 37 8 10
-23 11 34 38 9
-24 12 35 39 10
-25 11 13 36 27
-26 1 12 37 28
-27 44 25 16 49
-28 45 26 17 50
-29 46 14 18 51
-30 47 15 19 52
-31 48 16 40 20
-32 49 17 41 21
-33 22 50 18 42
-34 23 51 19 43
-35 44 24 52 20
-36 45 25 40 21
-37 22 46 26 41
-38 23 14 47 42
-39 24 15 48 43
-40 36 58 61 31
-41 37 59 62 32
-42 33 38 60 63
-43 34 39 61 64
-44 35 27 62 65
-45 36 28 63 53
-46 37 29 64 54
-47 55 38 30 65
-48 56 39 31 53
-49 57 27 32 54
-50 33 55 58 28
-51 34 56 59 29
-52 35 57 60 30
-53 45 69 48 76
-54 77 46 70 49
-55 78 47 71 50
-56 66 48 72 51
-57 67 49 73 52
-58 68 50 40 74
-59 69 51 41 75
-60 70 52 42 76
-61 77 71 40 43
-62 44 78 72 41
-63 66 45 73 42
-64 67 46 74 43
-65 44 68 47 75
-66 56 7 8 63
-67 57 8 9 64
-68 58 9 10 65
-69 11 59 53 10
-70 11 12 60 54
-71 55 12 13 61
-72 1 56 13 62
-73 1 2 57 63
-74 2 3 58 64
-75 3 4 59 65
-76 4 5 60 53
-77 5 6 61 54
-78 55 6 7 62
0

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