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On this page are computer-accessible forms for the graph C4[ 126, 2 ] = C_126(1,55).

(I) Following is a form readable by MAGMA:

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

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

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

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