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On this page are computer-accessible forms for the graph C4[ 126, 9 ] = 2AT[ 126, 1 ].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {104, 105} under the group generated by the following permutations:

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

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

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

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