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On this page are computer-accessible forms for the graph C4[ 120, 6 ] = C_120(1,41).

(I) Following is a form readable by MAGMA:

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

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

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