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On this page are computer-accessible forms for the graph C4[ 84, 5 ] = PS(12,7;2).

(I) Following is a form readable by MAGMA:

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

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

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

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