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On this page are computer-accessible forms for the graph C4[ 82, 1 ] = W(41,2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

a: (14, 55)
b: (32, 73)
c: (7, 48)
d: (31, 72)
e: (13, 54)
f: (38, 79)
g: (40, 81)
h: (27, 68)
m: (17, 58)
n1: (34, 75)
a1: (25, 66)
b1: (30, 71)
c1: (6, 47)
d1: (3, 44)
e1: (37, 78)
f1: (10, 51)
g1: (35, 76)
h1: (15, 56)
m1: (22, 63)
n2: (29, 70)
a2: (23, 64)
b2: (2, 43)
c2: (16, 57)
d2: (19, 60)
e2: (11, 52)
f2: (24, 65)
g2: (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)
h2: (9, 50)
m2: (2, 41)(3, 40)(4, 39)(5, 38)(6, 37)(7, 36)(8, 35)(9, 34)(10, 33)(11, 32)(12, 31)(13, 30)(14, 29)(15, 28)(16, 27)(17, 26)(18, 25)(19, 24)(20, 23)(21, 22)(43, 82)(44, 81)(45, 80)(46, 79)(47, 78)(48, 77)(49, 76)(50, 75)(51, 74)(52, 73)(53, 72)(54, 71)(55, 70)(56, 69)(57, 68)(58, 67)(59, 66)(60, 65)(61, 64)(62, 63)
n3: (4, 45)
a3: (39, 80)
b3: (41, 82)
c3: (5, 46)
d3: (12, 53)
e3: (33, 74)
f3: (28, 69)
g3: (36, 77)
h3: (26, 67)
m3: (18, 59)
n4: (8, 49)
a4: (21, 62)

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

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