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On this page are computer-accessible forms for the graph C4[ 114, 3 ] = PS(6,19;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {76, 77} under the group generated by the following permutations:

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

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

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