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On this page are computer-accessible forms for the graph C4[ 120, 37 ] = UG(ATD[120,54]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 17} under the group generated by the following permutations:

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

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

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