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On this page are computer-accessible forms for the graph C4[ 81, 4 ] = PS(3,27;8).

(I) Following is a form readable by MAGMA:

g:=Graph<81|{ {27, 28}, {48, 56}, {54, 62}, {53, 61}, {52, 60}, {51, 59}, {50, 58}, {49, 57}, {36, 55}, {44, 63}, {40, 59}, {41, 60}, {43, 62}, {42, 61}, {47, 55}, {4, 30}, {5, 31}, {1, 29}, {3, 31}, {2, 30}, {37, 56}, {39, 58}, {2, 28}, {3, 29}, {38, 57}, {28, 63}, {4, 32}, {15, 43}, {14, 42}, {13, 41}, {12, 40}, {7, 35}, {6, 34}, {5, 33}, {20, 48}, {21, 49}, {22, 50}, {23, 51}, {18, 55}, {26, 63}, {24, 61}, {6, 32}, {15, 41}, {14, 40}, {7, 33}, {22, 48}, {23, 49}, {25, 62}, {8, 34}, {13, 39}, {12, 38}, {9, 35}, {24, 50}, {25, 51}, {19, 56}, {23, 60}, {8, 36}, {26, 54}, {11, 39}, {10, 38}, {9, 37}, {16, 60}, {17, 61}, {18, 62}, {19, 63}, {24, 52}, {25, 53}, {20, 57}, {22, 59}, {10, 36}, {27, 53}, {11, 37}, {26, 52}, {21, 58}, {12, 56}, {15, 59}, {14, 58}, {13, 57}, {1, 54}, {16, 42}, {17, 43}, {20, 46}, {21, 47}, {11, 55}, {16, 44}, {17, 45}, {18, 46}, {19, 47}, {18, 44}, {19, 45}, {1, 65}, {15, 79}, {14, 78}, {13, 77}, {12, 76}, {11, 75}, {10, 74}, {9, 73}, {8, 72}, {7, 71}, {6, 70}, {5, 69}, {4, 68}, {3, 67}, {2, 66}, {16, 80}, {17, 81}, {8, 79}, {1, 72}, {7, 78}, {5, 76}, {3, 74}, {2, 73}, {6, 77}, {4, 75}, {30, 76}, {31, 77}, {20, 64}, {21, 65}, {22, 66}, {23, 67}, {28, 74}, {29, 75}, {9, 80}, {10, 81}, {27, 64}, {24, 68}, {27, 71}, {26, 70}, {25, 69}, {29, 64}, {31, 66}, {30, 65}, {32, 67}, {44, 79}, {40, 75}, {36, 71}, {33, 68}, {43, 78}, {41, 76}, {35, 70}, {34, 69}, {42, 77}, {37, 72}, {47, 66}, {45, 64}, {39, 74}, {32, 78}, {33, 79}, {38, 73}, {46, 65}, {34, 80}, {35, 81}, {48, 67}, {52, 71}, {49, 68}, {51, 70}, {50, 69}, {45, 80}, {53, 72}, {46, 81}, {54, 73} }>;

(II) A more general form is to represent the graph as the orbit of {27, 28} under the group generated by the following permutations:

a: (1, 28, 55)(2, 47, 65)(3, 39, 75)(4, 31, 58)(5, 50, 68)(6, 42, 78)(7, 34, 61)(8, 53, 71)(9, 45, 81)(10, 37, 64)(11, 29, 74)(12, 48, 57)(13, 40, 67)(14, 32, 77)(15, 51, 60)(16, 43, 70)(17, 35, 80)(18, 54, 63)(19, 46, 73)(20, 38, 56)(21, 30, 66)(22, 49, 76)(23, 41, 59)(24, 33, 69)(25, 52, 79)(26, 44, 62)(27, 36, 72)
b: (2, 27)(3, 26)(4, 25)(5, 24)(6, 23)(7, 22)(8, 21)(9, 20)(10, 19)(11, 18)(12, 17)(13, 16)(14, 15)(29, 54)(30, 53)(31, 52)(32, 51)(33, 50)(34, 49)(35, 48)(36, 47)(37, 46)(38, 45)(39, 44)(40, 43)(41, 42)(56, 81)(57, 80)(58, 79)(59, 78)(60, 77)(61, 76)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)
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, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81)

(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[ 81, 4 ]
81
-1 72 29 54 65
-2 66 28 73 30
-3 67 29 74 31
-4 68 30 75 32
-5 33 69 31 76
-6 77 34 70 32
-7 33 78 35 71
-8 34 79 36 72
-9 35 80 37 73
-10 36 81 38 74
-11 55 37 39 75
-12 56 38 40 76
-13 77 57 39 41
-14 78 58 40 42
-15 79 59 41 43
-16 44 80 60 42
-17 45 81 61 43
-18 44 55 46 62
-19 45 56 47 63
-20 46 57 48 64
-21 47 58 49 65
-22 66 48 59 50
-23 67 49 60 51
-24 68 50 61 52
-25 69 51 62 53
-26 70 52 63 54
-27 71 28 53 64
-28 2 27 63 74
-29 1 3 64 75
-30 2 4 65 76
-31 66 77 3 5
-32 67 78 4 6
-33 68 79 5 7
-34 69 80 6 8
-35 70 81 7 9
-36 55 71 8 10
-37 11 56 72 9
-38 12 57 73 10
-39 11 13 58 74
-40 12 14 59 75
-41 13 15 60 76
-42 77 14 16 61
-43 78 15 17 62
-44 79 16 18 63
-45 80 17 19 64
-46 81 18 20 65
-47 55 66 19 21
-48 22 56 67 20
-49 23 57 68 21
-50 22 24 58 69
-51 23 25 59 70
-52 24 26 60 71
-53 25 27 61 72
-54 1 26 62 73
-55 11 36 47 18
-56 12 37 48 19
-57 13 38 49 20
-58 14 39 50 21
-59 22 15 40 51
-60 23 16 41 52
-61 24 17 42 53
-62 25 18 43 54
-63 44 26 28 19
-64 45 27 29 20
-65 1 46 30 21
-66 22 2 47 31
-67 23 3 48 32
-68 33 24 4 49
-69 34 25 5 50
-70 35 26 6 51
-71 36 27 7 52
-72 1 37 8 53
-73 2 38 9 54
-74 3 28 39 10
-75 11 4 29 40
-76 12 5 30 41
-77 13 6 31 42
-78 14 7 32 43
-79 33 44 15 8
-80 34 45 16 9
-81 35 46 17 10
0

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