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On this page are computer-accessible forms for the graph C4[ 117, 4 ] = PS(9,13;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 53} under the group generated by the following permutations:

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

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

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