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On this page are computer-accessible forms for the graph C4[ 80, 9 ] = MPS(8,20;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {20, 22} under the group generated by the following permutations:

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

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

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