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On this page are computer-accessible forms for the graph C4[ 125, 4 ] = PS(5,25;4).

(I) Following is a form readable by MAGMA:

g:=Graph<125|{ {25, 26}, {48, 52}, {50, 54}, {49, 53}, {68, 77}, {70, 79}, {69, 78}, {100, 111}, {96, 107}, {97, 108}, {99, 110}, {96, 110}, {97, 111}, {67, 76}, {98, 109}, {64, 80}, {75, 91}, {74, 90}, {73, 89}, {72, 88}, {71, 87}, {70, 86}, {69, 85}, {68, 84}, {67, 83}, {66, 82}, {65, 81}, {98, 112}, {99, 113}, {32, 53}, {34, 55}, {40, 61}, {42, 63}, {100, 114}, {33, 54}, {71, 80}, {41, 62}, {2, 26}, {7, 31}, {6, 30}, {5, 29}, {4, 28}, {3, 27}, {72, 81}, {74, 83}, {1, 27}, {5, 31}, {4, 30}, {35, 56}, {73, 82}, {39, 60}, {47, 51}, {32, 61}, {34, 63}, {36, 57}, {38, 59}, {2, 28}, {3, 29}, {33, 62}, {75, 84}, {37, 58}, {64, 98}, {65, 99}, {27, 56}, {31, 60}, {80, 116}, {89, 125}, {88, 124}, {83, 119}, {82, 118}, {81, 117}, {28, 57}, {30, 59}, {6, 32}, {66, 100}, {15, 41}, {14, 40}, {7, 33}, {22, 48}, {23, 49}, {29, 58}, {80, 119}, {8, 32}, {15, 39}, {14, 38}, {13, 37}, {12, 36}, {11, 35}, {10, 34}, {9, 33}, {24, 48}, {25, 49}, {81, 120}, {85, 124}, {83, 122}, {8, 34}, {13, 39}, {12, 38}, {9, 35}, {24, 50}, {31, 52}, {86, 125}, {82, 121}, {84, 120}, {87, 123}, {86, 122}, {85, 121}, {26, 55}, {30, 51}, {10, 36}, {11, 37}, {84, 123}, {87, 101}, {95, 109}, {94, 108}, {91, 105}, {90, 104}, {1, 50}, {93, 104}, {95, 106}, {92, 106}, {93, 107}, {94, 105}, {16, 40}, {19, 43}, {18, 42}, {17, 41}, {20, 44}, {21, 45}, {22, 46}, {23, 47}, {77, 116}, {79, 118}, {16, 42}, {17, 43}, {20, 46}, {21, 47}, {78, 117}, {92, 103}, {76, 112}, {79, 115}, {78, 114}, {77, 113}, {91, 102}, {18, 44}, {89, 103}, {88, 102}, {19, 45}, {76, 115}, {90, 101}, {26, 72}, {27, 73}, {28, 74}, {29, 75}, {55, 96}, {56, 97}, {58, 99}, {57, 98}, {62, 96}, {63, 97}, {59, 100}, {7, 101}, {61, 95}, {60, 94}, {57, 91}, {56, 90}, {53, 87}, {52, 86}, {19, 113}, {18, 112}, {15, 109}, {14, 108}, {11, 105}, {10, 104}, {22, 116}, {23, 117}, {35, 64}, {39, 68}, {43, 72}, {36, 65}, {46, 75}, {38, 67}, {44, 73}, {12, 106}, {59, 93}, {58, 92}, {51, 85}, {13, 107}, {20, 114}, {21, 115}, {37, 66}, {45, 74}, {52, 93}, {54, 95}, {1, 107}, {17, 123}, {16, 122}, {5, 111}, {4, 110}, {43, 64}, {53, 94}, {47, 68}, {40, 69}, {46, 67}, {42, 71}, {44, 65}, {2, 108}, {55, 89}, {54, 88}, {19, 125}, {18, 124}, {9, 103}, {8, 102}, {3, 109}, {24, 118}, {25, 119}, {41, 70}, {51, 92}, {45, 66}, {60, 76}, {63, 79}, {62, 78}, {61, 77}, {20, 101}, {22, 103}, {24, 105}, {21, 102}, {25, 106}, {48, 69}, {50, 71}, {6, 112}, {15, 121}, {14, 120}, {7, 113}, {49, 70}, {1, 120}, {5, 124}, {3, 122}, {8, 114}, {13, 119}, {12, 118}, {9, 115}, {2, 121}, {6, 125}, {10, 116}, {17, 111}, {16, 110}, {11, 117}, {4, 123}, {23, 104} }>;

(II) A more general form is to represent the graph as the orbit of {25, 26} 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, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125)
b: (1, 26, 51, 76, 101)(2, 47, 67, 87, 107)(3, 43, 58, 98, 113)(4, 39, 74, 84, 119)(5, 35, 65, 95, 125)(6, 31, 56, 81, 106)(7, 27, 72, 92, 112)(8, 48, 63, 78, 118)(9, 44, 54, 89, 124)(10, 40, 70, 100, 105)(11, 36, 61, 86, 111)(12, 32, 52, 97, 117)(13, 28, 68, 83, 123)(14, 49, 59, 94, 104)(15, 45, 75, 80, 110)(16, 41, 66, 91, 116)(17, 37, 57, 77, 122)(18, 33, 73, 88, 103)(19, 29, 64, 99, 109)(20, 50, 55, 85, 115)(21, 46, 71, 96, 121)(22, 42, 62, 82, 102)(23, 38, 53, 93, 108)(24, 34, 69, 79, 114)(25, 30, 60, 90, 120)
c: (2, 25)(3, 24)(4, 23)(5, 22)(6, 21)(7, 20)(8, 19)(9, 18)(10, 17)(11, 16)(12, 15)(13, 14)(27, 50)(28, 49)(29, 48)(30, 47)(31, 46)(32, 45)(33, 44)(34, 43)(35, 42)(36, 41)(37, 40)(38, 39)(52, 75)(53, 74)(54, 73)(55, 72)(56, 71)(57, 70)(58, 69)(59, 68)(60, 67)(61, 66)(62, 65)(63, 64)(77, 100)(78, 99)(79, 98)(80, 97)(81, 96)(82, 95)(83, 94)(84, 93)(85, 92)(86, 91)(87, 90)(88, 89)(102, 125)(103, 124)(104, 123)(105, 122)(106, 121)(107, 120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)

(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[ 125, 4 ]
125
-1 27 50 107 120
-2 121 26 28 108
-3 122 27 29 109
-4 110 123 28 30
-5 111 124 29 31
-6 112 125 30 32
-7 33 101 113 31
-8 34 102 114 32
-9 33 35 103 115
-10 34 36 104 116
-11 35 37 105 117
-12 36 38 106 118
-13 37 39 107 119
-14 38 40 108 120
-15 121 39 41 109
-16 110 122 40 42
-17 111 123 41 43
-18 44 112 124 42
-19 45 113 125 43
-20 44 46 101 114
-21 45 47 102 115
-22 46 48 103 116
-23 47 49 104 117
-24 48 50 105 118
-25 26 49 106 119
-26 55 2 25 72
-27 1 56 3 73
-28 2 57 4 74
-29 3 58 5 75
-30 4 59 6 51
-31 5 60 7 52
-32 6 61 8 53
-33 7 62 9 54
-34 55 8 63 10
-35 11 56 9 64
-36 12 57 10 65
-37 11 66 13 58
-38 12 67 14 59
-39 13 68 15 60
-40 14 69 16 61
-41 15 70 17 62
-42 16 71 18 63
-43 17 72 19 64
-44 18 73 20 65
-45 66 19 74 21
-46 22 67 20 75
-47 23 68 51 21
-48 22 24 69 52
-49 23 25 70 53
-50 1 24 71 54
-51 47 92 30 85
-52 48 93 31 86
-53 49 94 32 87
-54 33 88 50 95
-55 34 89 26 96
-56 35 90 27 97
-57 36 91 28 98
-58 99 37 92 29
-59 100 38 93 30
-60 39 94 31 76
-61 77 40 95 32
-62 33 78 41 96
-63 34 79 42 97
-64 35 80 43 98
-65 44 99 36 81
-66 45 100 37 82
-67 46 38 83 76
-68 77 47 39 84
-69 78 48 40 85
-70 79 49 41 86
-71 80 50 42 87
-72 88 26 81 43
-73 44 89 27 82
-74 45 90 28 83
-75 46 91 29 84
-76 67 112 60 115
-77 68 113 61 116
-78 69 114 62 117
-79 70 115 63 118
-80 71 116 64 119
-81 72 117 65 120
-82 66 121 73 118
-83 67 122 74 119
-84 68 123 75 120
-85 121 69 124 51
-86 122 70 125 52
-87 101 123 71 53
-88 102 124 72 54
-89 55 103 125 73
-90 56 101 104 74
-91 57 102 105 75
-92 58 103 51 106
-93 59 104 52 107
-94 60 105 53 108
-95 61 106 54 109
-96 55 110 62 107
-97 56 111 63 108
-98 57 112 64 109
-99 110 58 113 65
-100 66 111 59 114
-101 90 7 20 87
-102 88 91 8 21
-103 22 89 92 9
-104 23 90 93 10
-105 11 24 91 94
-106 12 25 92 95
-107 1 13 93 96
-108 2 14 94 97
-109 3 15 95 98
-110 99 4 16 96
-111 100 5 17 97
-112 6 18 76 98
-113 77 99 7 19
-114 78 100 8 20
-115 79 9 21 76
-116 22 77 80 10
-117 11 23 78 81
-118 12 24 79 82
-119 13 25 80 83
-120 1 14 81 84
-121 2 15 82 85
-122 3 16 83 86
-123 4 17 84 87
-124 88 5 18 85
-125 89 6 19 86
0

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