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On this page are computer-accessible forms for the graph C4[ 126, 5 ] = PS(6,21;2).

(I) Following is a form readable by MAGMA:

g:=Graph<126|{ {41, 43}, {21, 22}, {104, 109}, {42, 44}, {105, 110}, {80, 88}, {81, 89}, {82, 90}, {83, 91}, {84, 92}, {103, 108}, {80, 93}, {102, 107}, {82, 95}, {81, 94}, {101, 106}, {96, 112}, {105, 121}, {104, 120}, {103, 119}, {102, 118}, {101, 117}, {100, 116}, {97, 113}, {98, 114}, {99, 115}, {32, 51}, {40, 59}, {36, 55}, {75, 88}, {79, 92}, {2, 22}, {3, 23}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {33, 52}, {41, 60}, {35, 54}, {76, 89}, {78, 91}, {1, 23}, {8, 30}, {9, 31}, {32, 55}, {42, 61}, {40, 63}, {34, 53}, {77, 90}, {77, 85}, {78, 86}, {79, 87}, {33, 56}, {39, 62}, {37, 60}, {35, 58}, {2, 24}, {100, 126}, {3, 25}, {6, 28}, {7, 29}, {96, 122}, {97, 123}, {34, 57}, {38, 61}, {4, 24}, {5, 25}, {6, 26}, {7, 27}, {37, 56}, {39, 58}, {64, 93}, {66, 95}, {72, 85}, {74, 87}, {4, 26}, {99, 125}, {5, 27}, {98, 124}, {36, 59}, {38, 57}, {65, 94}, {73, 86}, {64, 98}, {65, 99}, {68, 102}, {69, 103}, {67, 96}, {71, 100}, {75, 104}, {68, 97}, {70, 99}, {76, 105}, {88, 125}, {66, 100}, {67, 101}, {86, 112}, {87, 113}, {94, 120}, {95, 121}, {69, 98}, {89, 126}, {22, 62}, {23, 63}, {25, 48}, {31, 54}, {29, 52}, {27, 50}, {10, 32}, {11, 33}, {14, 36}, {15, 37}, {88, 114}, {89, 115}, {92, 118}, {93, 119}, {1, 42}, {30, 53}, {26, 49}, {87, 124}, {12, 32}, {13, 33}, {14, 34}, {15, 35}, {29, 48}, {31, 50}, {72, 101}, {74, 103}, {86, 123}, {12, 34}, {13, 35}, {70, 104}, {71, 105}, {90, 116}, {91, 117}, {28, 51}, {30, 49}, {73, 102}, {85, 122}, {90, 106}, {91, 107}, {92, 108}, {93, 109}, {94, 110}, {95, 111}, {24, 43}, {28, 47}, {83, 96}, {16, 36}, {17, 37}, {18, 38}, {19, 39}, {25, 44}, {27, 46}, {84, 97}, {16, 38}, {17, 39}, {24, 47}, {26, 45}, {23, 46}, {18, 40}, {19, 41}, {85, 111}, {22, 45}, {20, 40}, {21, 41}, {20, 42}, {11, 106}, {21, 116}, {13, 108}, {15, 110}, {17, 112}, {19, 114}, {14, 108}, {15, 109}, {18, 112}, {19, 113}, {14, 109}, {18, 113}, {12, 106}, {13, 107}, {20, 114}, {21, 115}, {12, 107}, {47, 72}, {20, 115}, {55, 80}, {44, 69}, {46, 71}, {56, 81}, {58, 83}, {45, 70}, {57, 82}, {43, 68}, {47, 64}, {59, 84}, {63, 80}, {48, 65}, {54, 71}, {52, 69}, {50, 67}, {56, 73}, {58, 75}, {60, 77}, {62, 79}, {4, 119}, {53, 70}, {49, 66}, {8, 123}, {57, 74}, {61, 78}, {1, 117}, {2, 118}, {3, 119}, {8, 124}, {9, 125}, {10, 126}, {1, 116}, {3, 118}, {9, 124}, {11, 126}, {2, 117}, {51, 68}, {10, 125}, {59, 76}, {48, 73}, {54, 79}, {52, 77}, {50, 75}, {43, 81}, {46, 84}, {49, 74}, {53, 78}, {4, 120}, {5, 121}, {6, 122}, {7, 123}, {60, 64}, {61, 65}, {62, 66}, {63, 67}, {5, 120}, {7, 122}, {16, 110}, {45, 83}, {44, 82}, {17, 111}, {6, 121}, {55, 72}, {51, 76}, {16, 111} }>;

(II) A more general form is to represent the graph as the orbit of {41, 43} under the group generated by the following permutations:

a: (2, 44, 101, 20)(3, 90, 63, 21)(4, 52, 55, 19)(5, 11, 59, 62)(6, 9, 51, 87)(7, 10, 97, 49)(12, 18, 45, 48)(13, 16, 58, 94)(14, 17, 104, 56)(22, 25, 106, 40)(23, 116)(24, 69, 72, 114)(26, 29, 32, 113)(27, 126, 84, 66)(28, 124)(30, 123)(31, 76, 79, 121)(33, 36, 39, 120)(34, 112, 70, 73)(35, 110)(37, 109)(38, 83, 65, 107)(41, 119, 77, 80)(42, 117)(43, 103, 85, 88)(46, 100)(47, 98)(50, 89, 92, 95)(53, 86)(54, 105)(57, 96, 99, 102)(60, 93)(61, 91)(67, 115, 118, 82)(68, 74, 122, 125)(75, 81, 108, 111)
b: (1, 22, 4, 121, 46, 79, 103, 82)(2, 26, 5, 71, 92, 74, 44, 116)(3, 66)(6, 27, 54, 108, 57, 42, 21, 24)(7, 31, 13, 34, 61, 115, 43, 28)(8, 29, 11, 107, 53, 65, 89, 68)(9, 33, 12, 78, 99, 81, 51, 123)(10, 73)(14, 38, 20, 41, 47, 122, 50, 35)(15, 36, 18, 114, 60, 72, 96, 75)(16, 40, 19, 64, 85, 67, 58, 109)(17, 80)(23, 62, 119, 95)(25, 100, 118, 49)(30, 48, 126, 102)(32, 86, 125, 56)(37, 55, 112, 88)(39, 93, 111, 63)(45, 120, 105, 84, 87, 69, 90, 117)(52, 106, 91, 70, 94, 76, 97, 124)(59, 113, 98, 77, 101, 83, 104, 110)
c: (2, 90)(3, 44)(4, 52)(5, 48)(6, 56)(7, 94)(8, 15)(9, 104)(10, 58)(11, 45)(12, 62)(13, 49)(14, 87)(16, 97)(17, 51)(18, 59)(19, 55)(20, 63)(21, 101)(22, 106)(23, 42)(24, 77)(26, 33)(27, 65)(28, 37)(29, 120)(30, 35)(31, 70)(32, 39)(34, 79)(36, 113)(38, 84)(41, 72)(43, 85)(46, 61)(47, 60)(50, 99)(53, 54)(57, 92)(66, 107)(67, 115)(68, 111)(69, 119)(71, 78)(73, 121)(74, 108)(75, 125)(76, 112)(80, 114)(81, 122)(82, 118)(83, 126)(86, 105)(89, 96)(91, 100)(93, 98)(95, 102)(109, 124)(110, 123)(116, 117)
d: (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, 126)
e: (3, 21)(4, 43)(5, 89)(6, 51)(7, 10)(11, 50)(12, 96)(13, 58)(14, 17)(18, 57)(19, 103)(20, 44)(22, 118)(23, 116)(25, 115)(26, 68)(27, 126)(29, 125)(30, 123)(32, 122)(33, 75)(34, 112)(36, 111)(37, 109)(39, 108)(40, 82)(41, 119)(45, 102)(46, 100)(48, 99)(49, 97)(52, 88)(53, 86)(55, 85)(56, 104)(59, 95)(60, 93)(62, 92)(63, 90)(66, 84)(67, 106)(69, 114)(70, 73)(74, 113)(76, 121)(77, 80)(81, 120)(83, 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.

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

&Graph
C4[ 126, 5 ]
126
-1 23 116 117 42
-2 22 24 117 118
-3 23 25 118 119
-4 24 26 119 120
-5 121 25 27 120
-6 121 122 26 28
-7 122 123 27 29
-8 123 124 28 30
-9 124 125 29 31
-10 125 126 30 32
-11 33 126 106 31
-12 34 106 107 32
-13 33 35 107 108
-14 34 36 108 109
-15 110 35 37 109
-16 110 111 36 38
-17 111 112 37 39
-18 112 113 38 40
-19 113 114 39 41
-20 114 115 40 42
-21 22 115 116 41
-22 45 2 62 21
-23 1 46 3 63
-24 2 47 4 43
-25 44 3 48 5
-26 45 4 49 6
-27 46 5 50 7
-28 47 6 51 8
-29 48 7 52 9
-30 49 8 53 10
-31 11 50 9 54
-32 55 12 51 10
-33 11 56 13 52
-34 12 57 14 53
-35 13 58 15 54
-36 55 14 59 16
-37 56 15 60 17
-38 57 16 61 18
-39 58 17 62 19
-40 59 18 63 20
-41 60 19 21 43
-42 44 1 61 20
-43 24 68 81 41
-44 25 69 82 42
-45 22 26 70 83
-46 23 27 71 84
-47 24 28 72 64
-48 25 29 73 65
-49 66 26 30 74
-50 67 27 31 75
-51 68 28 32 76
-52 33 77 69 29
-53 34 78 70 30
-54 35 79 71 31
-55 36 80 72 32
-56 33 37 81 73
-57 34 38 82 74
-58 35 39 83 75
-59 36 40 84 76
-60 77 37 41 64
-61 78 38 42 65
-62 22 66 79 39
-63 23 67 80 40
-64 47 60 93 98
-65 99 48 61 94
-66 100 49 62 95
-67 101 50 63 96
-68 102 51 97 43
-69 44 103 52 98
-70 99 45 104 53
-71 100 46 105 54
-72 55 101 47 85
-73 56 102 48 86
-74 57 103 49 87
-75 88 58 104 50
-76 89 59 105 51
-77 90 60 52 85
-78 91 61 53 86
-79 92 62 54 87
-80 55 88 93 63
-81 56 89 94 43
-82 44 57 90 95
-83 45 58 91 96
-84 46 59 92 97
-85 77 111 122 72
-86 78 112 123 73
-87 79 113 124 74
-88 80 114 125 75
-89 81 115 126 76
-90 77 82 116 106
-91 78 83 117 107
-92 79 84 118 108
-93 80 64 119 109
-94 110 81 65 120
-95 66 121 111 82
-96 67 122 112 83
-97 68 123 113 84
-98 69 124 114 64
-99 70 125 115 65
-100 66 71 126 116
-101 67 72 106 117
-102 68 73 107 118
-103 69 74 108 119
-104 70 75 109 120
-105 110 121 71 76
-106 11 12 90 101
-107 12 13 91 102
-108 13 14 92 103
-109 14 15 93 104
-110 15 16 94 105
-111 16 17 95 85
-112 17 18 96 86
-113 18 19 97 87
-114 88 19 20 98
-115 99 89 20 21
-116 1 100 90 21
-117 1 2 101 91
-118 2 3 102 92
-119 3 4 103 93
-120 4 5 104 94
-121 5 6 105 95
-122 6 7 85 96
-123 7 8 86 97
-124 8 9 87 98
-125 88 99 9 10
-126 11 89 100 10
0

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