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On this page are computer-accessible forms for the graph C4[ 120, 23 ] = PL(MC3(4,15,1,4,7,10,1),[10^6,12^5]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {56, 63} under the group generated by the following permutations:

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

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

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