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On this page are computer-accessible forms for the graph C4[ 84, 21 ] = SDD(C_21(1,8)).

(I) Following is a form readable by MAGMA:

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

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

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

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