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On this page are computer-accessible forms for the graph C4[ 80, 1 ] = W(40,2).

(I) Following is a form readable by MAGMA:

g:=Graph<80|{ {2, 3}, {78, 79}, {76, 77}, {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}, {74, 75}, {1, 2}, {77, 78}, {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}, {73, 74}, {3, 4}, {75, 76}, {27, 28}, {11, 12}, {19, 20}, {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}, {8, 47}, {24, 63}, {16, 55}, {1, 40}, {23, 62}, {22, 63}, {21, 60}, {20, 61}, {19, 58}, {2, 43}, {3, 42}, {4, 45}, {5, 44}, {6, 47}, {7, 46}, {16, 57}, {17, 56}, {18, 59}, {1, 42}, {22, 61}, {21, 62}, {2, 41}, {5, 46}, {6, 45}, {17, 58}, {18, 57}, {3, 44}, {20, 59}, {19, 60}, {4, 43}, {7, 48}, {15, 56}, {8, 49}, {9, 48}, {10, 51}, {11, 50}, {12, 53}, {13, 52}, {14, 55}, {15, 54}, {9, 50}, {10, 49}, {13, 54}, {14, 53}, {11, 52}, {31, 32}, {12, 51}, {1, 80}, {23, 64}, {31, 72}, {24, 65}, {30, 71}, {29, 68}, {28, 69}, {27, 66}, {26, 67}, {25, 64}, {31, 70}, {25, 66}, {30, 69}, {29, 70}, {26, 65}, {27, 68}, {28, 67}, {32, 71}, {40, 79}, {32, 73}, {33, 72}, {34, 75}, {35, 74}, {36, 77}, {37, 76}, {38, 79}, {39, 78}, {33, 74}, {34, 73}, {37, 78}, {38, 77}, {35, 76}, {36, 75}, {39, 80}, {41, 80}, {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: (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)
b: (29, 69)
c: (4, 44)
d: (2, 42)
e: (31, 71)
f: (17, 57)
g: (6, 46)
h: (11, 51)
m: (25, 65)
n1: (2, 40)(3, 39)(4, 38)(5, 37)(6, 36)(7, 35)(8, 34)(9, 33)(10, 32)(11, 31)(12, 30)(13, 29)(14, 28)(15, 27)(16, 26)(17, 25)(18, 24)(19, 23)(20, 22)(42, 80)(43, 79)(44, 78)(45, 77)(46, 76)(47, 75)(48, 74)(49, 73)(50, 72)(51, 71)(52, 70)(53, 69)(54, 68)(55, 67)(56, 66)(57, 65)(58, 64)(59, 63)(60, 62)
a1: (8, 48)
b1: (21, 61)
c1: (27, 67)
d1: (7, 47)
e1: (22, 62)
f1: (23, 63)
g1: (37, 77)
h1: (39, 79)
m1: (30, 70)
n2: (33, 73)
a2: (35, 75)
b2: (3, 43)
c2: (26, 66)
d2: (16, 56)
e2: (14, 54)
f2: (40, 80)
g2: (13, 53)
h2: (24, 64)
m2: (32, 72)
n3: (34, 74)
a3: (15, 55)
b3: (38, 78)
c3: (9, 49)
d3: (36, 76)
e3: (20, 60)
f3: (28, 68)
g3: (5, 45)
h3: (18, 58)
m3: (10, 50)
n4: (12, 52)

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

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