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On this page are computer-accessible forms for the graph C4[ 120, 31 ] = PL(Br(6,10;3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 61} under the group generated by the following permutations:

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

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

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