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On this page are computer-accessible forms for the graph C4[ 120, 5 ] = C_120(1,31).

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

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