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On this page are computer-accessible forms for the graph C4[ 80, 26 ] = SDD({4,4}_4,2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 51} under the group generated by the following permutations:

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

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

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