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On this page are computer-accessible forms for the graph C4[ 126, 4 ] = PS(18,7;2).

(I) Following is a form readable by MAGMA:

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

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

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

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