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On this page are computer-accessible forms for the graph C4[ 81, 3 ] = PS(9,9;2).

(I) Following is a form readable by MAGMA:

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

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

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

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