Graph forms
for C4 [ 140, 8 ] = PL(Br(14,5;2))
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On this page are computer-accessible forms for the graph C4[ 140, 8 ] =
PL(Br(14,5;2)).
(I) Following is a form readable by MAGMA:
g:=Graph<140|{ {67, 71}, {66, 71}, {68, 85}, {66, 84}, {67, 85}, {67, 84}, {65,
97}, {64, 97}, {67, 98}, {64, 98}, {65, 98}, {68, 98}, {69, 99}, {68, 99}, {68,
112}, {69, 113}, {69, 112}, {70, 113}, {70, 126}, {70, 127}, {69, 126}, {65,
125}, {66, 127}, {65, 126}, {25, 89}, {61, 125}, {60, 124}, {27, 91}, {43, 107},
{11, 74}, {60, 125}, {27, 90}, {24, 89}, {42, 107}, {11, 73}, {24, 90}, {25,
90}, {61, 126}, {2, 71}, {12, 73}, {1, 71}, {59, 125}, {28, 90}, {12, 74}, {42,
108}, {28, 91}, {59, 124}, {43, 108}, {17, 89}, {33, 105}, {50, 122}, {51, 123},
{1, 72}, {32, 105}, {17, 88}, {50, 123}, {2, 72}, {32, 106}, {18, 88}, {49,
123}, {18, 89}, {33, 106}, {49, 122}, {55, 124}, {38, 106}, {39, 107}, {55,
123}, {38, 107}, {39, 106}, {6, 72}, {62, 112}, {7, 73}, {6, 73}, {63, 112}, {7,
72}, {51, 124}, {5, 85}, {63, 111}, {7, 87}, {40, 120}, {41, 121}, {4, 85}, {62,
111}, {31, 78}, {7, 86}, {40, 121}, {4, 86}, {31, 77}, {5, 86}, {41, 122}, {35,
119}, {59, 111}, {58, 110}, {45, 121}, {58, 111}, {59, 110}, {14, 88}, {27, 77},
{26, 76}, {54, 96}, {15, 88}, {27, 76}, {26, 77}, {45, 122}, {55, 96}, {15, 87},
{57, 97}, {53, 109}, {14, 87}, {57, 96}, {21, 76}, {52, 109}, {16, 74}, {58,
96}, {22, 76}, {17, 75}, {52, 110}, {16, 75}, {58, 97}, {35, 120}, {17, 74},
{53, 110}, {48, 108}, {49, 109}, {22, 75}, {48, 109}, {49, 108}, {8, 86}, {21,
75}, {39, 121}, {8, 87}, {39, 120}, {3, 99}, {21, 117}, {20, 116}, {2, 99}, {20,
117}, {51, 82}, {51, 81}, {21, 118}, {42, 79}, {52, 81}, {2, 100}, {19, 117},
{41, 79}, {52, 82}, {3, 100}, {31, 120}, {19, 116}, {13, 101}, {31, 119}, {30,
118}, {55, 95}, {12, 101}, {61, 84}, {30, 119}, {54, 95}, {12, 102}, {62, 84},
{57, 83}, {56, 82}, {37, 79}, {36, 78}, {29, 119}, {13, 102}, {57, 82}, {56,
83}, {37, 78}, {36, 79}, {29, 118}, {8, 100}, {25, 117}, {9, 101}, {8, 101},
{62, 83}, {32, 77}, {9, 100}, {32, 78}, {61, 83}, {48, 94}, {25, 118}, {48, 95},
{1, 113}, {23, 103}, {45, 93}, {47, 95}, {22, 103}, {44, 93}, {47, 94}, {44,
94}, {1, 114}, {45, 94}, {5, 113}, {29, 105}, {28, 104}, {19, 103}, {18, 102},
{18, 103}, {29, 104}, {28, 105}, {19, 102}, {5, 114}, {10, 114}, {37, 93}, {35,
91}, {11, 115}, {10, 115}, {37, 92}, {34, 91}, {41, 80}, {9, 115}, {38, 92},
{42, 80}, {4, 127}, {15, 116}, {9, 114}, {38, 93}, {3, 127}, {15, 115}, {22,
104}, {34, 92}, {46, 80}, {47, 81}, {11, 116}, {35, 92}, {23, 104}, {46, 81},
{47, 80}, {3, 128}, {4, 128}, {6, 128}, {6, 129}, {10, 128}, {10, 129}, {13,
129}, {14, 130}, {13, 130}, {14, 129}, {16, 130}, {16, 131}, {23, 132}, {23,
131}, {20, 130}, {20, 131}, {30, 132}, {24, 131}, {30, 133}, {24, 132}, {26,
132}, {26, 133}, {36, 134}, {36, 135}, {43, 136}, {33, 133}, {34, 134}, {44,
136}, {46, 136}, {33, 134}, {34, 133}, {46, 137}, {44, 135}, {43, 135}, {40,
134}, {40, 135}, {56, 138}, {56, 139}, {63, 140}, {63, 139}, {60, 138}, {60,
139}, {50, 136}, {50, 137}, {53, 137}, {54, 138}, {53, 138}, {54, 137}, {70,
140}, {64, 139}, {64, 140}, {66, 140} }>;
(II) A more general form is to represent the graph as the orbit of {67, 71}
under the group generated by the following permutations:
a: (6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 61)(12, 62)(13, 63)(14, 64)(15,
65)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 51)(22, 52)(23, 53)(24, 54)(25,
55)(26, 46)(27, 47)(28, 48)(29, 49)(30, 50)(31, 41)(32, 42)(33, 43)(34, 44)(35,
45)(71, 72)(73, 84)(74, 83)(75, 82)(76, 81)(77, 80)(78, 79)(85, 86)(87, 98)(88,
97)(89, 96)(90, 95)(91, 94)(92, 93)(99, 100)(101, 112)(102, 111)(103, 110)(104,
109)(105, 108)(106, 107)(113, 114)(115, 126)(116, 125)(117, 124)(118, 123)(119,
122)(120, 121)(127, 128)(129, 140)(130, 139)(131, 138)(132, 137)(133, 136)(134,
135) (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.
**************
&Graph **************
b: (1, 2)(3, 5)(6, 7)(8, 10)(11, 12)(13, 15)(16, 17)(18, 20)(21, 22)(23, 25)(26,
27)(28, 30)(31, 32)(33, 35)(36, 37)(38, 40)(41, 42)(43, 45)(46, 47)(48, 50)(51,
52)(53, 55)(56, 57)(58, 60)(61, 62)(63, 65)(66, 67)(68, 70)(85, 127)(86,
128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95,
137)(96, 138)(97, 139)(98, 140)(99, 113)(100, 114)(101, 115)(102, 116)(103,
117)(104, 118)(105, 119)(106, 120)(107, 121)(108, 122)(109, 123)(110, 124)(111,
125)(112, 126)
c: (1, 6, 12, 17, 21, 26, 32, 37, 41, 46, 52, 57, 61, 66, 2, 7, 11, 16, 22, 27,
31, 36, 42, 47, 51, 56, 62, 67)(3, 8, 15, 20, 23, 28, 35, 40, 43, 48, 55, 60,
63, 68, 5, 10, 13, 18, 25, 30, 33, 38, 45, 50, 53, 58, 65, 70)(4, 9, 14, 19, 24,
29, 34, 39, 44, 49, 54, 59, 64, 69)(71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84)(85, 114, 129, 102, 89, 118, 133, 106, 93, 122, 137, 110, 97, 126,
127, 100, 87, 116, 131, 104, 91, 120, 135, 108, 95, 124, 139, 112)(86, 115, 130,
103, 90, 119, 134, 107, 94, 123, 138, 111, 98, 113, 128, 101, 88, 117, 132, 105,
92, 121, 136, 109, 96, 125, 140, 99)
d: (2, 5)(3, 4)(6, 10)(7, 9)(12, 15)(13, 14)(16, 20)(17, 19)(22, 25)(23, 24)(26,
30)(27, 29)(32, 35)(33, 34)(36, 40)(37, 39)(42, 45)(43, 44)(46, 50)(47, 49)(52,
55)(53, 54)(56, 60)(57, 59)(62, 65)(63, 64)(66, 70)(67, 69)(71, 113)(72,
114)(73, 115)(74, 116)(75, 117)(76, 118)(77, 119)(78, 120)(79, 121)(80, 122)(81,
123)(82, 124)(83, 125)(84, 126)(85, 99)(86, 100)(87, 101)(88, 102)(89, 103)(90,
104)(91, 105)(92, 106)(93, 107)(94, 108)(95, 109)(96, 110)(97, 111)(98, 112)
C4[ 140, 8 ]
140
-1 113 114 71 72
-2 99 100 71 72
-3 99 100 127 128
-4 127 128 85 86
-5 113 114 85 86
-6 72 73 128 129
-7 72 73 86 87
-8 100 101 86 87
-9 100 101 114 115
-10 114 115 128 129
-11 115 116 73 74
-12 101 102 73 74
-13 101 102 129 130
-14 88 129 130 87
-15 88 115 116 87
-16 74 75 130 131
-17 88 89 74 75
-18 88 89 102 103
-19 102 103 116 117
-20 116 117 130 131
-21 117 118 75 76
-22 103 104 75 76
-23 132 103 104 131
-24 132 89 90 131
-25 89 90 117 118
-26 77 132 133 76
-27 77 90 91 76
-28 90 91 104 105
-29 104 105 118 119
-30 132 133 118 119
-31 77 78 119 120
-32 77 78 105 106
-33 133 134 105 106
-34 133 134 91 92
-35 91 92 119 120
-36 78 79 134 135
-37 78 79 92 93
-38 92 93 106 107
-39 121 106 107 120
-40 121 134 135 120
-41 121 122 79 80
-42 79 80 107 108
-43 135 136 107 108
-44 135 136 93 94
-45 121 122 93 94
-46 80 81 136 137
-47 80 81 94 95
-48 94 95 108 109
-49 122 123 108 109
-50 122 123 136 137
-51 123 124 81 82
-52 110 81 82 109
-53 110 137 138 109
-54 137 138 95 96
-55 123 124 95 96
-56 82 83 138 139
-57 82 83 96 97
-58 110 111 96 97
-59 110 111 124 125
-60 124 125 138 139
-61 125 126 83 84
-62 111 112 83 84
-63 111 112 139 140
-64 139 140 97 98
-65 125 126 97 98
-66 71 127 84 140
-67 71 84 85 98
-68 99 112 85 98
-69 99 112 113 126
-70 113 126 127 140
-71 66 1 67 2
-72 1 2 6 7
-73 11 12 6 7
-74 11 12 16 17
-75 22 16 17 21
-76 22 26 27 21
-77 26 27 31 32
-78 36 37 31 32
-79 36 37 41 42
-80 46 47 41 42
-81 46 47 51 52
-82 56 57 51 52
-83 56 57 61 62
-84 66 67 61 62
-85 67 68 4 5
-86 4 5 7 8
-87 14 15 7 8
-88 14 15 17 18
-89 24 25 17 18
-90 24 25 27 28
-91 34 35 27 28
-92 34 35 37 38
-93 44 45 37 38
-94 44 45 47 48
-95 55 47 48 54
-96 55 57 58 54
-97 57 58 64 65
-98 67 68 64 65
-99 2 68 3 69
-100 2 3 8 9
-101 12 13 8 9
-102 12 13 18 19
-103 22 23 18 19
-104 22 23 28 29
-105 33 28 29 32
-106 33 38 39 32
-107 38 39 42 43
-108 48 49 42 43
-109 48 49 52 53
-110 58 59 52 53
-111 58 59 62 63
-112 68 69 62 63
-113 1 69 70 5
-114 1 5 9 10
-115 11 15 9 10
-116 11 15 19 20
-117 25 19 20 21
-118 25 29 30 21
-119 35 29 30 31
-120 35 39 40 31
-121 45 39 40 41
-122 45 49 50 41
-123 55 49 50 51
-124 55 59 60 51
-125 59 60 61 65
-126 69 70 61 65
-127 66 3 4 70
-128 3 4 6 10
-129 13 14 6 10
-130 13 14 16 20
-131 23 24 16 20
-132 23 24 26 30
-133 33 34 26 30
-134 33 34 36 40
-135 44 36 40 43
-136 44 46 50 43
-137 46 50 53 54
-138 56 60 53 54
-139 56 60 63 64
-140 66 70 63 64
0