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On this page are computer-accessible forms for the graph C4[ 80, 15 ] = PL(MC3(4,10,1,9,3,0,1),[4^10,10^4]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {37, 45} under the group generated by the following permutations:

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

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

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