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On this page are computer-accessible forms for the graph C4[ 120, 40 ] = UG(ATD[120,58]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {12, 13} under the group generated by the following permutations:

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

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