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On this page are computer-accessible forms for the graph C4[ 84, 22 ] = SDD(PS(3,7;2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {38, 54} under the group generated by the following permutations:

a: (43, 64)
b: (44, 65)
c: (55, 76)
d: (2, 9)(3, 31)(4, 32)(5, 37)(6, 14)(7, 38)(8, 21)(10, 41)(11, 22)(12, 42)(15, 33)(16, 34)(17, 20)(23, 36)(24, 30)(25, 27)(43, 51)(44, 54)(45, 56)(46, 52)(48, 62)(50, 59)(53, 58)(61, 63)(64, 72)(65, 75)(66, 77)(67, 73)(69, 83)(71, 80)(74, 79)(82, 84)
e: (45, 66)
f: (1, 2)(3, 4)(5, 25)(6, 26)(7, 28)(8, 27)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 19)(16, 20)(29, 30)(31, 42)(32, 41)(33, 39)(34, 40)(35, 38)(36, 37)(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)
g: (52, 73)
h: (2, 4)(5, 20)(6, 23)(7, 41)(8, 35)(10, 11)(13, 21)(15, 37)(16, 38)(17, 30)(18, 25)(19, 29)(22, 34)(24, 33)(27, 39)(28, 40)(44, 58)(46, 54)(47, 50)(48, 52)(49, 55)(53, 62)(56, 61)(57, 59)(65, 79)(67, 75)(68, 71)(69, 73)(70, 76)(74, 83)(77, 82)(78, 80)
m: (63, 84)
n1: (58, 79)
a1: (59, 80)
b1: (50, 71)
c1: (61, 82)
d1: (46, 67)
e1: (51, 72)
f1: (54, 75)
g1: (62, 83)
h1: (49, 70)
m1: (57, 78)
n2: (56, 77)
a2: (53, 74)
b2: (60, 81)

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

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