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On this page are computer-accessible forms for the graph C4[ 84, 7 ] = PS(6,28;5).

(I) Following is a form readable by MAGMA:

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

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

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

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