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On this page are computer-accessible forms for the graph C4[ 120, 67 ] = BGCG(UG(ATD[60,16]);K1;{13,14}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {58, 61} under the group generated by the following permutations:

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

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

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