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On this page are computer-accessible forms for the graph C4[ 84, 6 ] = PS(3,28;3).

(I) Following is a form readable by MAGMA:

g:=Graph<84|{ {28, 29}, {56, 59}, {55, 58}, {54, 57}, {32, 57}, {38, 63}, {36, 61}, {34, 59}, {4, 31}, {37, 62}, {33, 58}, {2, 31}, {3, 30}, {1, 30}, {35, 60}, {32, 63}, {2, 29}, {29, 60}, {31, 62}, {3, 32}, {30, 61}, {27, 56}, {15, 44}, {11, 40}, {7, 36}, {19, 48}, {23, 52}, {4, 33}, {15, 42}, {14, 43}, {13, 40}, {12, 41}, {7, 34}, {6, 35}, {5, 32}, {20, 49}, {21, 48}, {22, 51}, {23, 50}, {24, 61}, {26, 63}, {5, 34}, {14, 41}, {13, 42}, {6, 33}, {21, 50}, {22, 49}, {25, 62}, {8, 35}, {28, 55}, {12, 39}, {23, 60}, {24, 51}, {8, 37}, {27, 54}, {11, 38}, {10, 39}, {9, 36}, {20, 57}, {22, 59}, {24, 53}, {25, 52}, {26, 55}, {9, 38}, {16, 63}, {10, 37}, {21, 58}, {25, 54}, {26, 53}, {11, 58}, {15, 62}, {13, 60}, {10, 57}, {14, 61}, {12, 59}, {1, 56}, {16, 43}, {20, 47}, {16, 45}, {18, 47}, {17, 44}, {19, 46}, {17, 46}, {18, 45}, {2, 67}, {16, 81}, {14, 79}, {12, 77}, {10, 75}, {8, 73}, {6, 71}, {4, 69}, {18, 83}, {1, 66}, {17, 82}, {13, 78}, {9, 74}, {5, 70}, {3, 68}, {11, 76}, {19, 84}, {4, 79}, {31, 84}, {1, 76}, {30, 83}, {3, 78}, {2, 77}, {29, 82}, {7, 72}, {17, 64}, {27, 74}, {19, 66}, {21, 68}, {23, 70}, {25, 72}, {18, 65}, {26, 73}, {22, 69}, {5, 80}, {7, 82}, {6, 81}, {28, 75}, {20, 67}, {8, 83}, {27, 64}, {9, 84}, {28, 65}, {15, 80}, {24, 71}, {33, 64}, {53, 84}, {51, 82}, {49, 80}, {47, 78}, {45, 76}, {43, 74}, {41, 72}, {39, 70}, {37, 68}, {35, 66}, {34, 65}, {50, 81}, {46, 77}, {42, 73}, {38, 69}, {36, 67}, {55, 80}, {52, 83}, {47, 72}, {44, 75}, {39, 64}, {40, 65}, {56, 81}, {46, 71}, {44, 69}, {42, 67}, {41, 66}, {45, 70}, {40, 71}, {43, 68}, {48, 73}, {54, 79}, {52, 77}, {50, 75}, {49, 74}, {53, 78}, {48, 79}, {51, 76} }>;

(II) A more general form is to represent the graph as the orbit of {28, 29} under the group generated by the following permutations:

a: (2, 28)(3, 27)(4, 26)(5, 25)(6, 24)(7, 23)(8, 22)(9, 21)(10, 20)(11, 19)(12, 18)(13, 17)(14, 16)(30, 56)(31, 55)(32, 54)(33, 53)(34, 52)(35, 51)(36, 50)(37, 49)(38, 48)(39, 47)(40, 46)(41, 45)(42, 44)(58, 84)(59, 83)(60, 82)(61, 81)(62, 80)(63, 79)(64, 78)(65, 77)(66, 76)(67, 75)(68, 74)(69, 73)(70, 72)
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, 79, 80, 81, 82, 83, 84)
c: (1, 29, 57)(2, 32, 66, 28, 54, 76)(3, 35, 75, 27, 51, 67)(4, 38, 84, 26, 48, 58)(5, 41, 65, 25, 45, 77)(6, 44, 74, 24, 42, 68)(7, 47, 83, 23, 39, 59)(8, 50, 64, 22, 36, 78)(9, 53, 73, 21, 33, 69)(10, 56, 82, 20, 30, 60)(11, 31, 63, 19, 55, 79)(12, 34, 72, 18, 52, 70)(13, 37, 81, 17, 49, 61)(14, 40, 62, 16, 46, 80)(15, 43, 71)

(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.

**************

&Graph
C4[ 84, 6 ]
84
-1 66 56 30 76
-2 77 67 29 31
-3 78 68 30 32
-4 33 79 69 31
-5 34 80 70 32
-6 33 35 81 71
-7 34 36 82 72
-8 35 37 83 73
-9 36 38 84 74
-10 57 37 39 75
-11 58 38 40 76
-12 77 59 39 41
-13 78 60 40 42
-14 79 61 41 43
-15 44 80 62 42
-16 45 81 63 43
-17 44 46 82 64
-18 45 47 83 65
-19 66 46 48 84
-20 67 57 47 49
-21 68 58 48 50
-22 69 59 49 51
-23 70 60 50 52
-24 71 61 51 53
-25 72 62 52 54
-26 55 73 63 53
-27 56 74 64 54
-28 55 29 75 65
-29 2 60 82 28
-30 1 3 61 83
-31 2 4 62 84
-32 57 3 5 63
-33 58 4 6 64
-34 59 5 7 65
-35 66 60 6 8
-36 67 61 7 9
-37 68 62 8 10
-38 11 69 63 9
-39 12 70 64 10
-40 11 13 71 65
-41 66 12 14 72
-42 67 13 15 73
-43 68 14 16 74
-44 69 15 17 75
-45 70 16 18 76
-46 77 71 17 19
-47 78 72 18 20
-48 79 73 19 21
-49 22 80 74 20
-50 23 81 75 21
-51 22 24 82 76
-52 77 23 25 83
-53 78 24 26 84
-54 57 79 25 27
-55 58 80 26 28
-56 1 59 81 27
-57 20 10 32 54
-58 11 33 55 21
-59 22 12 34 56
-60 23 13 35 29
-61 24 14 36 30
-62 25 15 37 31
-63 26 16 38 32
-64 33 27 17 39
-65 34 28 18 40
-66 1 35 19 41
-67 2 36 20 42
-68 3 37 21 43
-69 22 44 4 38
-70 23 45 5 39
-71 24 46 6 40
-72 25 47 7 41
-73 26 48 8 42
-74 27 49 9 43
-75 44 28 50 10
-76 11 1 45 51
-77 12 2 46 52
-78 13 3 47 53
-79 14 4 48 54
-80 55 15 5 49
-81 56 16 6 50
-82 17 7 29 51
-83 18 8 30 52
-84 19 9 31 53
0

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