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On this page are computer-accessible forms for the graph C4[ 125, 5 ] = PS(5,25;9).

(I) Following is a form readable by MAGMA:

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

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

**************

&Graph
C4[ 125, 5 ]
125
-1 112 27 115 50
-2 113 26 28 116
-3 114 27 29 117
-4 115 28 30 118
-5 116 29 31 119
-6 117 30 32 120
-7 33 121 118 31
-8 34 122 119 32
-9 33 35 123 120
-10 121 34 36 124
-11 122 35 37 125
-12 101 123 36 38
-13 102 124 37 39
-14 103 125 38 40
-15 101 104 39 41
-16 102 105 40 42
-17 103 106 41 43
-18 44 104 107 42
-19 45 105 108 43
-20 44 46 106 109
-21 110 45 47 107
-22 111 46 48 108
-23 112 47 49 109
-24 110 113 48 50
-25 111 26 114 49
-26 67 2 25 60
-27 1 68 3 61
-28 2 69 4 62
-29 3 70 5 63
-30 4 71 6 64
-31 5 72 7 65
-32 66 6 73 8
-33 67 7 74 9
-34 68 8 75 10
-35 11 69 51 9
-36 12 70 52 10
-37 11 13 71 53
-38 12 14 72 54
-39 55 13 15 73
-40 56 14 16 74
-41 57 15 17 75
-42 58 16 18 51
-43 59 17 19 52
-44 60 18 20 53
-45 61 19 21 54
-46 22 55 62 20
-47 23 56 63 21
-48 22 24 57 64
-49 23 25 58 65
-50 66 1 24 59
-51 35 82 95 42
-52 36 83 96 43
-53 44 37 84 97
-54 45 38 85 98
-55 99 46 39 86
-56 100 47 40 87
-57 88 48 41 76
-58 77 89 49 42
-59 78 90 50 43
-60 44 79 91 26
-61 45 80 92 27
-62 46 81 93 28
-63 47 82 94 29
-64 48 83 95 30
-65 49 84 96 31
-66 50 85 97 32
-67 33 26 86 98
-68 99 34 27 87
-69 88 100 35 28
-70 89 36 29 76
-71 77 90 37 30
-72 78 91 38 31
-73 79 92 39 32
-74 33 80 93 40
-75 34 81 94 41
-76 122 57 70 105
-77 123 58 71 106
-78 124 59 72 107
-79 125 60 73 108
-80 101 61 74 109
-81 110 102 62 75
-82 111 103 51 63
-83 112 104 52 64
-84 113 105 53 65
-85 66 114 106 54
-86 55 67 115 107
-87 56 68 116 108
-88 57 69 117 109
-89 110 58 70 118
-90 111 59 71 119
-91 112 60 72 120
-92 121 113 61 73
-93 122 114 62 74
-94 123 115 63 75
-95 124 116 51 64
-96 125 117 52 65
-97 66 101 118 53
-98 67 102 119 54
-99 55 68 103 120
-100 121 56 69 104
-101 12 80 15 97
-102 13 81 16 98
-103 99 14 82 17
-104 100 15 83 18
-105 16 84 19 76
-106 77 17 85 20
-107 78 18 86 21
-108 22 79 19 87
-109 88 23 80 20
-110 89 24 81 21
-111 22 90 25 82
-112 1 23 91 83
-113 2 24 92 84
-114 3 25 93 85
-115 1 4 94 86
-116 2 5 95 87
-117 88 3 6 96
-118 89 4 7 97
-119 90 5 8 98
-120 99 91 6 9
-121 100 92 7 10
-122 11 93 8 76
-123 77 12 94 9
-124 78 13 95 10
-125 11 79 14 96
0

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