Graph forms
for C4 [ 162, 16 ] = UG(ATD[162,26])
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On this page are computer-accessible forms for the graph C4[ 162, 16 ] =
UG(ATD[162,26]).
(I) Following is a form readable by MAGMA:
g:=Graph<162|{ {42, 43}, {108, 109}, {60, 62}, {136, 139}, {16, 20}, {154, 158},
{34, 38}, {64, 68}, {1, 4}, {131, 134}, {10, 15}, {89, 92}, {105, 108}, {1, 7},
{144, 150}, {96, 103}, {136, 143}, {129, 134}, {21, 29}, {130, 138}, {22, 30},
{66, 74}, {4, 13}, {145, 152}, {116, 125}, {49, 59}, {51, 57}, {1, 10}, {135,
140}, {67, 72}, {86, 93}, {52, 56}, {147, 159}, {83, 95}, {48, 61}, {149, 154},
{1, 16}, {13, 28}, {4, 22}, {43, 57}, {79, 92}, {97, 114}, {7, 19}, {42, 62},
{102, 114}, {73, 92}, {143, 153}, {8, 31}, {133, 146}, {64, 87}, {71, 80}, {105,
126}, {111, 119}, {129, 153}, {99, 121}, {4, 31}, {47, 51}, {128, 157}, {7, 25},
{40, 54}, {102, 120}, {107, 117}, {111, 113}, {6, 25}, {39, 56}, {21, 53}, {75,
107}, {81, 113}, {86, 119}, {10, 40}, {19, 49}, {12, 46}, {89, 123}, {133, 161},
{7, 34}, {18, 55}, {65, 100}, {13, 43}, {77, 107}, {87, 113}, {14, 39}, {88,
113}, {74, 96}, {81, 123}, {17, 58}, {137, 162}, {28, 55}, {76, 96}, {95, 115},
{64, 109}, {71, 104}, {81, 126}, {10, 58}, {13, 61}, {9, 56}, {78, 127}, {81,
96}, {94, 111}, {3, 49}, {23, 37}, {93, 110}, {75, 127}, {148, 160}, {70, 115},
{19, 37}, {28, 36}, {68, 126}, {74, 112}, {15, 52}, {67, 120}, {80, 108}, {16,
46}, {68, 122}, {84, 106}, {91, 101}, {2, 61}, {159, 160}, {19, 44}, {73, 118},
{93, 98}, {15, 79}, {33, 97}, {26, 90}, {54, 119}, {61, 127}, {63, 125}, {29,
94}, {30, 93}, {20, 80}, {50, 118}, {32, 102}, {41, 111}, {35, 100}, {36, 99},
{27, 83}, {31, 87}, {33, 104}, {24, 82}, {54, 124}, {46, 100}, {14, 69}, {50,
121}, {20, 88}, {5, 72}, {54, 123}, {38, 107}, {31, 82}, {11, 70}, {27, 85},
{34, 109}, {16, 64}, {45, 125}, {9, 91}, {45, 127}, {32, 116}, {45, 121}, {25,
76}, {29, 72}, {55, 97}, {20, 67}, {39, 112}, {24, 79}, {6, 94}, {22, 78}, {2,
88}, {38, 125}, {38, 122}, {43, 118}, {59, 101}, {22, 73}, {46, 78}, {3, 98},
{40, 73}, {30, 124}, {23, 116}, {57, 90}, {37, 70}, {3, 103}, {48, 84}, {40,
76}, {30, 121}, {48, 87}, {15, 103}, {58, 82}, {26, 115}, {18, 120}, {41, 67},
{17, 122}, {44, 71}, {44, 65}, {32, 78}, {5, 106}, {36, 75}, {29, 114}, {58,
85}, {12, 124}, {24, 104}, {8, 122}, {55, 69}, {51, 65}, {35, 80}, {53, 70},
{28, 106}, {57, 79}, {52, 66}, {2, 117}, {34, 85}, {21, 98}, {59, 76}, {8, 112},
{42, 82}, {39, 95}, {32, 88}, {27, 99}, {23, 110}, {35, 90}, {62, 71}, {6, 124},
{14, 117}, {27, 103}, {25, 100}, {37, 91}, {24, 152}, {12, 141}, {17, 144}, {9,
140}, {3, 133}, {5, 130}, {26, 157}, {23, 159}, {6, 140}, {8, 130}, {2, 137},
{14, 133}, {12, 128}, {26, 148}, {11, 132}, {9, 154}, {50, 161}, {17, 132}, {11,
145}, {21, 137}, {63, 162}, {5, 154}, {18, 141}, {60, 158}, {45, 142}, {52,
145}, {47, 134}, {60, 150}, {11, 160}, {63, 147}, {41, 135}, {36, 148}, {56,
136}, {50, 131}, {18, 160}, {47, 157}, {35, 151}, {60, 136}, {63, 139}, {53,
128}, {33, 150}, {41, 158}, {47, 149}, {53, 143}, {48, 138}, {59, 135}, {62,
130}, {42, 151}, {33, 159}, {44, 147}, {51, 140}, {49, 142}, {83, 145}, {89,
155}, {91, 152}, {94, 157}, {69, 129}, {102, 162}, {95, 153}, {66, 138}, {92,
149}, {86, 155}, {72, 134}, {84, 155}, {77, 156}, {69, 144}, {84, 129}, {68,
146}, {66, 149}, {90, 141}, {74, 146}, {65, 152}, {89, 131}, {75, 144}, {85,
142}, {77, 146}, {110, 142}, {105, 139}, {118, 148}, {112, 150}, {99, 132}, {97,
139}, {101, 143}, {114, 153}, {104, 132}, {110, 128}, {117, 155}, {77, 162},
{120, 151}, {115, 131}, {123, 138}, {83, 161}, {108, 158}, {105, 156}, {86,
161}, {101, 156}, {126, 135}, {116, 141}, {106, 151}, {98, 156}, {119, 137},
{109, 147} }>;
(II) A more general form is to represent the graph as the orbit of {42, 43}
under the group generated by the following permutations:
a: (2, 3)(4, 7)(5, 9)(6, 8)(10, 16)(11, 18)(12, 17)(13, 19)(14, 21)(15, 20)(22,
34)(23, 36)(24, 35)(25, 31)(26, 33)(27, 32)(28, 37)(29, 39)(30, 38)(40, 64)(41,
66)(42, 65)(43, 44)(46, 58)(47, 60)(48, 59)(49, 61)(50, 63)(51, 62)(52, 67)(53,
69)(54, 68)(55, 70)(56, 72)(57, 71)(73, 109)(74, 111)(75, 110)(76, 87)(77,
86)(78, 85)(79, 80)(82, 100)(83, 102)(84, 101)(88, 103)(89, 105)(90, 104)(91,
106)(92, 108)(93, 107)(94, 112)(95, 114)(96, 113)(97, 115)(98, 117)(99,
116)(118, 147)(119, 146)(120, 145)(121, 125)(122, 124)(123, 126)(127, 142)(128,
144)(129, 143)(130, 140)(131, 139)(132, 141)(133, 137)(134, 136)(135, 138)(148,
159)(149, 158)(150, 157)(151, 152)(155, 156)(161, 162) (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)(4, 117, 103)(5, 115, 104)(6, 116, 105)(7, 88, 98)(8, 89, 99)(9, 90,
97)(10, 61, 133)(11, 62, 134)(12, 63, 135)(13, 14, 15)(16, 137, 49)(17, 138,
50)(18, 136, 51)(19, 20, 21)(22, 107, 96)(23, 108, 94)(24, 106, 95)(25, 32,
156)(26, 33, 154)(27, 31, 155)(28, 39, 79)(29, 37, 80)(30, 38, 81)(34, 113,
93)(35, 114, 91)(36, 112, 92)(40, 127, 146)(41, 128, 147)(42, 129, 145)(43, 69,
52)(44, 67, 53)(45, 68, 54)(46, 162, 59)(47, 160, 60)(48, 161, 58)(55, 56,
57)(64, 119, 142)(65, 120, 143)(66, 118, 144)(70, 71, 72)(73, 75, 74)(76, 78,
77)(82, 84, 83)(85, 87, 86)(100, 102, 101)(109, 111, 110)(121, 122, 123)(124,
125, 126)(130, 131, 132)(139, 140, 141)(148, 150, 149)(151, 153, 152)(157, 159,
158)
c: (1, 4, 13, 28, 55, 97, 139, 105, 126, 81, 123, 89, 131, 115, 70, 37, 19,
7)(2, 5, 14, 29, 56, 98, 140, 103, 124, 79, 121, 90, 132, 116, 71, 38, 20, 8)(3,
6, 15, 30, 57, 99, 141, 104, 125, 80, 122, 88, 130, 117, 72, 39, 21, 9)(10, 22,
43, 36, 18, 33, 63, 108, 68, 113, 138, 155, 134, 95, 53, 91, 49, 25)(11, 23, 44,
34, 16, 31, 61, 106, 69, 114, 136, 156, 135, 96, 54, 92, 50, 26)(12, 24, 45, 35,
17, 32, 62, 107, 67, 112, 137, 154, 133, 94, 52, 93, 51, 27)(40, 73, 118, 148,
160, 159, 147, 109, 64, 87, 48, 84, 129, 153, 143, 101, 59, 76)(41, 74, 119,
149, 161, 157, 145, 110, 65, 85, 46, 82, 127, 151, 144, 102, 60, 77)(42, 75,
120, 150, 162, 158, 146, 111, 66, 86, 47, 83, 128, 152, 142, 100, 58, 78)
d: (2, 3)(4, 10)(5, 11)(6, 12)(7, 16)(8, 17)(9, 18)(13, 15)(19, 20)(22, 40)(23,
41)(24, 42)(25, 46)(26, 47)(27, 48)(28, 52)(29, 53)(30, 54)(31, 58)(32, 59)(33,
60)(34, 64)(35, 65)(36, 66)(37, 67)(38, 68)(39, 69)(43, 79)(44, 80)(45, 81)(49,
88)(50, 89)(51, 90)(55, 56)(61, 103)(62, 104)(63, 105)(70, 72)(74, 75)(76,
78)(83, 84)(85, 87)(91, 120)(92, 118)(93, 119)(94, 128)(95, 129)(96, 127)(97,
136)(98, 137)(99, 138)(101, 102)(106, 145)(107, 146)(108, 147)(110, 111)(112,
144)(113, 142)(114, 143)(115, 134)(116, 135)(117, 133)(121, 123)(125, 126)(130,
132)(140, 141)(148, 149)(151, 152)(154, 160)(155, 161)(156, 162)(158, 159)
C4[ 162, 16 ]
162
-1 4 16 7 10
-2 88 137 61 117
-3 133 103 49 98
-4 22 1 13 31
-5 154 72 106 130
-6 25 124 94 140
-7 1 34 25 19
-8 122 112 31 130
-9 154 56 91 140
-10 1 58 15 40
-11 132 145 70 160
-12 46 124 128 141
-13 4 28 61 43
-14 133 69 39 117
-15 79 103 52 10
-16 1 46 20 64
-17 132 122 144 58
-18 55 160 141 120
-19 44 37 49 7
-20 88 67 80 16
-21 137 29 53 98
-22 78 4 73 30
-23 110 37 159 116
-24 79 82 104 152
-25 100 6 7 76
-26 90 157 115 148
-27 99 103 83 85
-28 55 13 36 106
-29 114 72 94 21
-30 22 121 124 93
-31 4 82 8 87
-32 88 78 102 116
-33 104 159 150 97
-34 38 7 85 109
-35 100 90 80 151
-36 99 148 28 75
-37 23 91 70 19
-38 34 122 125 107
-39 56 112 14 95
-40 73 10 54 76
-41 67 111 135 158
-42 82 62 151 43
-43 13 57 118 42
-44 147 71 19 65
-45 121 125 127 142
-46 12 78 100 16
-47 134 157 149 51
-48 61 138 84 87
-49 3 59 19 142
-50 121 161 118 131
-51 57 47 140 65
-52 66 56 145 15
-53 143 70 128 21
-54 123 124 40 119
-55 69 28 18 97
-56 136 39 52 9
-57 79 90 51 43
-58 82 17 85 10
-59 101 135 49 76
-60 136 158 62 150
-61 2 13 48 127
-62 60 71 42 130
-63 125 147 139 162
-64 68 16 87 109
-65 44 100 51 152
-66 138 149 52 74
-67 72 41 20 120
-68 122 146 126 64
-69 55 144 14 129
-70 11 37 115 53
-71 44 80 104 62
-72 67 134 5 29
-73 22 92 40 118
-74 66 112 146 96
-75 144 36 127 107
-76 25 59 40 96
-77 156 146 107 162
-78 22 46 127 32
-79 24 57 15 92
-80 35 71 20 108
-81 123 113 126 96
-82 24 58 31 42
-83 145 27 95 161
-84 155 48 106 129
-85 34 58 27 142
-86 155 93 161 119
-87 113 48 31 64
-88 2 113 20 32
-89 155 123 92 131
-90 35 57 26 141
-91 101 37 9 152
-92 89 79 149 73
-93 110 30 86 98
-94 111 157 6 29
-95 115 39 83 153
-96 81 103 74 76
-97 33 55 114 139
-98 156 3 93 21
-99 121 132 36 27
-100 35 46 25 65
-101 143 156 91 59
-102 114 162 32 120
-103 3 15 27 96
-104 33 132 24 71
-105 156 126 139 108
-106 5 28 84 151
-107 77 38 117 75
-108 80 158 105 109
-109 34 147 64 108
-110 23 93 128 142
-111 113 94 41 119
-112 39 150 8 74
-113 88 111 81 87
-114 102 29 97 153
-115 26 70 95 131
-116 23 125 141 32
-117 155 2 14 107
-118 148 50 73 43
-119 111 137 86 54
-120 67 102 18 151
-121 99 45 50 30
-122 68 38 17 8
-123 89 81 138 54
-124 12 6 30 54
-125 45 38 116 63
-126 68 135 81 105
-127 45 78 61 75
-128 110 12 157 53
-129 134 69 84 153
-130 5 138 62 8
-131 89 134 115 50
-132 11 99 104 17
-133 3 14 146 161
-134 47 72 129 131
-135 59 126 41 140
-136 143 56 60 139
-137 2 162 119 21
-138 66 123 48 130
-139 136 105 63 97
-140 135 6 51 9
-141 12 90 116 18
-142 110 45 49 85
-143 101 136 53 153
-144 69 17 150 75
-145 11 83 52 152
-146 77 133 68 74
-147 44 159 63 109
-148 36 26 160 118
-149 66 154 47 92
-150 33 144 112 60
-151 35 106 42 120
-152 24 145 91 65
-153 143 114 95 129
-154 158 5 149 9
-155 89 84 117 86
-156 77 101 105 98
-157 47 26 94 128
-158 154 60 41 108
-159 33 23 147 160
-160 11 148 159 18
-161 133 50 83 86
-162 77 102 137 63
0