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On this page are computer-accessible forms for the graph C4[ 120, 68 ] = BGCG(UG(ATD[60,16]);K1;{16,17}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {44, 61} under the group generated by the following permutations:

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

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

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