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On this page are computer-accessible forms for the graph C4[ 80, 10 ] = PS(4,40;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 42} under the group generated by the following permutations:

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

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

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