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On this page are computer-accessible forms for the graph C4[ 120, 16 ] = MPS(4,60;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {57, 61} under the group generated by the following permutations:

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

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

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