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On this page are computer-accessible forms for the graph C4[ 80, 7 ] = PS(16,5;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {9, 11} under the group generated by the following permutations:

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

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

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