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On this page are computer-accessible forms for the graph C4[ 117, 5 ] = PS(3,39;16).

(I) Following is a form readable by MAGMA:

g:=Graph<117|{ {39, 40}, {64, 80}, {78, 94}, {77, 93}, {76, 92}, {65, 81}, {66, 82}, {67, 83}, {68, 84}, {69, 85}, {70, 86}, {71, 87}, {72, 88}, {73, 89}, {74, 90}, {75, 91}, {64, 87}, {72, 95}, {65, 88}, {67, 90}, {69, 92}, {71, 94}, {66, 89}, {70, 93}, {68, 91}, {8, 46}, {25, 63}, {24, 62}, {9, 47}, {16, 54}, {17, 55}, {1, 41}, {23, 63}, {22, 62}, {21, 61}, {20, 60}, {19, 59}, {2, 42}, {3, 43}, {4, 44}, {5, 45}, {6, 46}, {7, 47}, {16, 56}, {17, 57}, {18, 58}, {73, 96}, {77, 100}, {75, 98}, {2, 40}, {23, 61}, {22, 60}, {19, 57}, {3, 41}, {6, 44}, {7, 45}, {18, 56}, {74, 97}, {78, 101}, {4, 42}, {21, 59}, {20, 58}, {5, 43}, {76, 99}, {8, 48}, {9, 49}, {10, 50}, {11, 51}, {12, 52}, {13, 53}, {14, 54}, {15, 55}, {10, 48}, {11, 49}, {14, 52}, {15, 53}, {12, 50}, {13, 51}, {42, 104}, {43, 105}, {46, 108}, {47, 109}, {50, 112}, {51, 113}, {54, 116}, {55, 117}, {19, 80}, {27, 88}, {23, 84}, {31, 92}, {35, 96}, {39, 100}, {20, 81}, {30, 91}, {28, 89}, {22, 83}, {36, 97}, {38, 99}, {44, 106}, {45, 107}, {52, 114}, {53, 115}, {21, 82}, {29, 90}, {37, 98}, {24, 80}, {31, 87}, {30, 86}, {29, 85}, {28, 84}, {27, 83}, {26, 82}, {25, 81}, {41, 96}, {43, 98}, {45, 100}, {47, 102}, {57, 112}, {59, 114}, {61, 116}, {42, 97}, {46, 101}, {58, 113}, {62, 117}, {24, 85}, {26, 87}, {40, 102}, {41, 103}, {1, 78}, {25, 86}, {44, 99}, {60, 115}, {48, 103}, {56, 111}, {23, 79}, {31, 71}, {30, 70}, {29, 69}, {28, 68}, {27, 67}, {26, 66}, {25, 65}, {24, 64}, {49, 104}, {51, 106}, {53, 108}, {55, 110}, {26, 64}, {31, 69}, {30, 68}, {27, 65}, {50, 105}, {54, 109}, {18, 79}, {28, 66}, {29, 67}, {48, 110}, {49, 111}, {52, 107}, {1, 96}, {21, 116}, {19, 114}, {3, 98}, {5, 100}, {7, 102}, {9, 104}, {11, 106}, {13, 108}, {15, 110}, {17, 112}, {2, 97}, {22, 117}, {6, 101}, {10, 105}, {14, 109}, {18, 113}, {1, 101}, {2, 102}, {3, 103}, {8, 108}, {9, 109}, {10, 110}, {11, 111}, {16, 116}, {17, 117}, {32, 70}, {33, 71}, {4, 99}, {20, 115}, {12, 107}, {32, 72}, {33, 73}, {34, 74}, {35, 75}, {36, 76}, {37, 77}, {38, 78}, {57, 80}, {59, 82}, {61, 84}, {63, 86}, {34, 72}, {35, 73}, {38, 76}, {39, 77}, {58, 81}, {62, 85}, {4, 104}, {5, 105}, {6, 106}, {7, 107}, {36, 74}, {37, 75}, {8, 103}, {60, 83}, {63, 79}, {40, 95}, {56, 79}, {32, 88}, {33, 89}, {34, 90}, {35, 91}, {36, 92}, {37, 93}, {38, 94}, {39, 95}, {12, 112}, {13, 113}, {14, 114}, {15, 115}, {32, 93}, {34, 95}, {16, 111}, {33, 94} }>;

(II) A more general form is to represent the graph as the orbit of {39, 40} under the group generated by the following permutations:

a: (2, 39)(3, 38)(4, 37)(5, 36)(6, 35)(7, 34)(8, 33)(9, 32)(10, 31)(11, 30)(12, 29)(13, 28)(14, 27)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(41, 78)(42, 77)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52, 67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(80, 117)(81, 116)(82, 115)(83, 114)(84, 113)(85, 112)(86, 111)(87, 110)(88, 109)(89, 108)(90, 107)(91, 106)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)
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, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117)
c: (1, 40, 79)(2, 56, 101)(3, 72, 84)(4, 49, 106)(5, 65, 89)(6, 42, 111)(7, 58, 94)(8, 74, 116)(9, 51, 99)(10, 67, 82)(11, 44, 104)(12, 60, 87)(13, 76, 109)(14, 53, 92)(15, 69, 114)(16, 46, 97)(17, 62, 80)(18, 78, 102)(19, 55, 85)(20, 71, 107)(21, 48, 90)(22, 64, 112)(23, 41, 95)(24, 57, 117)(25, 73, 100)(26, 50, 83)(27, 66, 105)(28, 43, 88)(29, 59, 110)(30, 75, 93)(31, 52, 115)(32, 68, 98)(33, 45, 81)(34, 61, 103)(35, 77, 86)(36, 54, 108)(37, 70, 91)(38, 47, 113)(39, 63, 96)

(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[ 117, 5 ]
117
-1 78 101 41 96
-2 102 40 42 97
-3 103 41 43 98
-4 44 99 104 42
-5 45 100 105 43
-6 44 46 101 106
-7 45 47 102 107
-8 46 48 103 108
-9 47 49 104 109
-10 110 48 50 105
-11 111 49 51 106
-12 112 50 52 107
-13 113 51 53 108
-14 114 52 54 109
-15 55 110 115 53
-16 56 111 116 54
-17 55 57 112 117
-18 56 79 58 113
-19 57 80 59 114
-20 58 81 60 115
-21 59 82 61 116
-22 60 83 62 117
-23 79 61 84 63
-24 80 62 85 64
-25 81 63 86 65
-26 66 82 64 87
-27 88 67 83 65
-28 66 89 68 84
-29 67 90 69 85
-30 68 91 70 86
-31 69 92 71 87
-32 88 70 93 72
-33 89 71 94 73
-34 90 72 95 74
-35 91 73 96 75
-36 92 74 97 76
-37 77 93 75 98
-38 99 78 94 76
-39 77 100 40 95
-40 2 102 39 95
-41 1 3 103 96
-42 2 4 104 97
-43 3 5 105 98
-44 99 4 6 106
-45 100 5 7 107
-46 101 6 8 108
-47 102 7 9 109
-48 110 103 8 10
-49 11 111 104 9
-50 12 112 105 10
-51 11 13 113 106
-52 12 14 114 107
-53 13 15 115 108
-54 14 16 116 109
-55 110 15 17 117
-56 111 79 16 18
-57 112 80 17 19
-58 113 81 18 20
-59 114 82 19 21
-60 22 115 83 20
-61 23 116 84 21
-62 22 24 117 85
-63 23 79 25 86
-64 24 80 26 87
-65 88 25 81 27
-66 89 26 82 28
-67 90 27 83 29
-68 91 28 84 30
-69 92 29 85 31
-70 93 30 86 32
-71 33 94 31 87
-72 88 34 95 32
-73 33 89 35 96
-74 34 90 36 97
-75 35 91 37 98
-76 99 36 92 38
-77 100 37 93 39
-78 1 101 38 94
-79 23 56 18 63
-80 24 57 19 64
-81 25 58 20 65
-82 66 26 59 21
-83 22 67 27 60
-84 23 68 28 61
-85 24 69 29 62
-86 25 70 30 63
-87 26 71 31 64
-88 27 72 32 65
-89 33 66 28 73
-90 34 67 29 74
-91 35 68 30 75
-92 36 69 31 76
-93 77 37 70 32
-94 33 78 38 71
-95 34 39 72 40
-96 1 35 73 41
-97 2 36 74 42
-98 3 37 75 43
-99 44 4 38 76
-100 77 45 5 39
-101 1 78 46 6
-102 2 47 7 40
-103 3 48 8 41
-104 4 49 9 42
-105 5 50 10 43
-106 11 44 6 51
-107 12 45 7 52
-108 13 46 8 53
-109 14 47 9 54
-110 55 15 48 10
-111 11 56 16 49
-112 12 57 17 50
-113 13 58 18 51
-114 14 59 19 52
-115 15 60 20 53
-116 16 61 21 54
-117 22 55 17 62
0

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