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On this page are computer-accessible forms for the graph C4[ 80, 27 ] = SDD(R_10(7,6)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {38, 54} under the group generated by the following permutations:

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

**************

&Graph
C4[ 80, 27 ]
80
-1 61 62 41 42
-2 70 50 61 41
-3 71 61 51 41
-4 61 41 74 54
-5 62 63 42 43
-6 72 62 52 42
-7 55 62 42 75
-8 44 63 64 43
-9 73 63 53 43
-10 56 63 43 76
-11 44 45 64 65
-12 44 74 64 54
-13 44 77 57 64
-14 66 45 46 65
-15 55 45 75 65
-16 45 78 58 65
-17 66 67 46 47
-18 66 56 46 76
-19 66 46 79 59
-20 67 68 47 48
-21 77 67 57 47
-22 67 47 80 60
-23 68 69 48 49
-24 68 48 71 51
-25 78 68 58 48
-26 69 70 49 50
-27 69 49 72 52
-28 79 69 59 49
-29 70 50 73 53
-30 80 70 60 50
-31 55 71 51 75
-32 77 57 71 51
-33 56 72 52 76
-34 78 58 72 52
-35 77 57 73 53
-36 79 59 73 53
-37 78 58 74 54
-38 80 60 74 54
-39 55 79 59 75
-40 56 80 60 76
-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 24 3 31 32
-52 33 34 27 6
-53 35 36 29 9
-54 12 4 37 38
-55 15 39 7 31
-56 33 18 40 10
-57 13 35 21 32
-58 34 25 37 16
-59 36 28 39 19
-60 22 38 40 30
-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 24 3 31 32
-72 33 34 27 6
-73 35 36 29 9
-74 12 4 37 38
-75 15 39 7 31
-76 33 18 40 10
-77 13 35 21 32
-78 34 25 37 16
-79 36 28 39 19
-80 22 38 40 30
0

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