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On this page are computer-accessible forms for the graph C4[ 126, 3 ] = DW(42,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {42, 43} under the group generated by the following permutations:

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

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

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