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On this page are computer-accessible forms for the graph C4[ 78, 5 ] = PS(6,13;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {13, 14} under the group generated by the following permutations:

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

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

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