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On this page are computer-accessible forms for the graph C4[ 80, 23 ] = SDD(W(10,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {34, 47} under the group generated by the following permutations:

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

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

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