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On this page are computer-accessible forms for the graph C4[ 84, 23 ] = BGCG(L(F28);K1;{1,2}).

(I) Following is a form readable by MAGMA:

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

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

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

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