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On this page are computer-accessible forms for the graph C4[ 123, 1 ] = C_123(1,40).

(I) Following is a form readable by MAGMA:

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

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