Graph forms
for C4 [ 165, 9 ] = UG(ATD[165,15])
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On this page are computer-accessible forms for the graph C4[ 165, 9 ] =
UG(ATD[165,15]).
(I) Following is a form readable by MAGMA:
g:=Graph<165|{ {74, 75}, {1, 3}, {160, 162}, {148, 150}, {16, 18}, {1, 2}, {132,
135}, {120, 123}, {24, 27}, {4, 7}, {3, 6}, {153, 156}, {147, 150}, {34, 39},
{2, 4}, {2, 5}, {162, 165}, {154, 157}, {146, 149}, {122, 125}, {11, 12}, {65,
70}, {5, 13}, {115, 123}, {7, 15}, {6, 14}, {84, 93}, {147, 154}, {146, 155},
{17, 27}, {133, 143}, {101, 111}, {100, 110}, {51, 57}, {50, 56}, {3, 8}, {128,
139}, {119, 124}, {113, 122}, {35, 40}, {7, 12}, {1, 12}, {150, 155}, {148,
153}, {131, 142}, {129, 140}, {116, 121}, {6, 11}, {4, 9}, {52, 58}, {102, 104},
{99, 109}, {5, 10}, {130, 141}, {16, 31}, {13, 28}, {15, 30}, {109, 127}, {1,
18}, {110, 125}, {37, 54}, {14, 29}, {136, 156}, {140, 152}, {137, 157}, {13,
24}, {15, 26}, {32, 54}, {39, 49}, {33, 55}, {14, 25}, {103, 112}, {71, 80}, {8,
16}, {10, 18}, {9, 17}, {78, 86}, {2, 27}, {108, 117}, {72, 81}, {8, 19}, {133,
158}, {12, 23}, {73, 82}, {36, 56}, {139, 151}, {38, 58}, {37, 57}, {9, 20},
{11, 22}, {10, 21}, {107, 116}, {32, 63}, {29, 60}, {31, 62}, {67, 98}, {68,
101}, {76, 109}, {78, 111}, {95, 125}, {30, 61}, {77, 110}, {79, 108}, {3, 39},
{135, 163}, {134, 162}, {133, 161}, {64, 101}, {132, 161}, {76, 106}, {28, 59},
{64, 104}, {65, 105}, {66, 106}, {67, 107}, {69, 108}, {26, 48}, {31, 53}, {30,
52}, {27, 49}, {143, 164}, {4, 40}, {82, 127}, {28, 50}, {29, 51}, {66, 114},
{17, 32}, {23, 38}, {21, 36}, {19, 34}, {79, 126}, {80, 97}, {26, 40}, {73,
123}, {84, 102}, {18, 33}, {22, 37}, {81, 98}, {67, 119}, {64, 117}, {149, 160},
{144, 165}, {24, 46}, {25, 47}, {74, 124}, {75, 125}, {20, 35}, {65, 118}, {90,
99}, {157, 164}, {19, 41}, {159, 165}, {23, 45}, {22, 44}, {73, 114}, {74, 113},
{68, 120}, {69, 121}, {5, 56}, {7, 58}, {66, 127}, {71, 122}, {20, 42}, {159,
161}, {25, 39}, {21, 43}, {92, 98}, {6, 57}, {156, 163}, {72, 119}, {79, 112},
{11, 75}, {32, 97}, {59, 113}, {62, 116}, {36, 105}, {38, 107}, {60, 114}, {61,
115}, {46, 97}, {48, 127}, {60, 115}, {35, 118}, {26, 77}, {55, 96}, {8, 80},
{10, 82}, {9, 81}, {57, 97}, {58, 98}, {59, 99}, {60, 100}, {61, 101}, {62,
102}, {63, 103}, {34, 126}, {62, 99}, {13, 109}, {15, 111}, {14, 110}, {17,
112}, {37, 68}, {35, 66}, {33, 64}, {42, 72}, {47, 77}, {46, 76}, {43, 73}, {34,
65}, {38, 69}, {44, 72}, {53, 80}, {55, 82}, {44, 74}, {45, 75}, {36, 67}, {54,
81}, {47, 70}, {48, 90}, {52, 94}, {49, 91}, {53, 95}, {50, 89}, {51, 88}, {40,
70}, {51, 93}, {50, 92}, {41, 71}, {46, 88}, {47, 89}, {16, 104}, {63, 71}, {22,
111}, {53, 76}, {55, 78}, {30, 100}, {45, 87}, {44, 86}, {41, 83}, {42, 84},
{49, 79}, {48, 78}, {43, 85}, {56, 70}, {28, 156}, {29, 157}, {41, 162}, {31,
141}, {25, 143}, {19, 139}, {21, 141}, {20, 140}, {23, 142}, {24, 135}, {61,
159}, {52, 144}, {59, 158}, {63, 153}, {43, 128}, {33, 142}, {45, 130}, {42,
146}, {54, 136}, {83, 145}, {86, 148}, {83, 144}, {96, 163}, {85, 145}, {86,
146}, {87, 147}, {85, 147}, {94, 152}, {93, 151}, {77, 134}, {92, 144}, {90,
149}, {94, 145}, {68, 151}, {83, 128}, {87, 131}, {94, 138}, {91, 143}, {92,
136}, {93, 137}, {84, 129}, {117, 160}, {95, 138}, {85, 130}, {91, 131}, {124,
164}, {123, 163}, {121, 161}, {88, 129}, {88, 132}, {89, 133}, {90, 134}, {91,
135}, {69, 152}, {95, 130}, {126, 160}, {105, 137}, {106, 138}, {105, 139},
{124, 158}, {108, 142}, {96, 131}, {126, 155}, {106, 140}, {107, 141}, {112,
152}, {114, 154}, {113, 153}, {116, 158}, {117, 159}, {118, 154}, {118, 155},
{100, 138}, {120, 136}, {103, 150}, {87, 164}, {102, 149}, {96, 148}, {103,
145}, {115, 132}, {120, 128}, {121, 129}, {89, 165}, {122, 134}, {119, 137},
{104, 151} }>;
(II) A more general form is to represent the graph as the orbit of {74, 75}
under the group generated by the following permutations:
a: (2, 12, 3, 18)(4, 11, 8, 10)(5, 7, 6, 16)(9, 75, 19, 82)(13, 58, 14, 104)(15,
57, 31, 56)(17, 45, 34, 55)(20, 74, 41, 73)(21, 40, 22, 80)(23, 39, 33, 27)(24,
38, 25, 64)(26, 37, 53, 36)(28, 52, 29, 102)(30, 51, 62, 50)(32, 130, 65,
78)(35, 44, 71, 43)(42, 113, 83, 114)(46, 107, 47, 101)(48, 54, 95, 105)(49,
142)(59, 144, 60, 84)(61, 88, 116, 89)(63, 85, 118, 86)(66, 72, 122, 128)(67,
77, 68, 76)(69, 143, 117, 135)(70, 111, 97, 141)(79, 131)(81, 125, 139, 127)(87,
126, 96, 112)(90, 136, 138, 137)(91, 108)(92, 100, 93, 99)(94, 157, 149,
156)(98, 110, 151, 109)(103, 147, 155, 148)(106, 119, 134, 120)(115, 129, 158,
165)(121, 133, 159, 132)(123, 140, 124, 162)(145, 154, 146, 153)(152, 164, 160,
163) (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, 27)(4, 18)(5, 12)(6, 24)(7, 10)(8, 17)(9, 16)(11, 13)(14, 135)(15,
82)(19, 112)(20, 104)(21, 58)(22, 109)(23, 56)(25, 91)(26, 55)(28, 75)(29,
132)(30, 73)(31, 81)(32, 80)(33, 40)(34, 79)(35, 64)(36, 38)(37, 76)(39, 49)(41,
103)(42, 102)(43, 52)(44, 99)(45, 50)(46, 57)(47, 131)(48, 78)(51, 88)(53,
54)(59, 74)(60, 115)(61, 114)(62, 72)(63, 71)(65, 108)(66, 101)(67, 107)(68,
106)(69, 105)(70, 142)(77, 96)(83, 145)(85, 144)(86, 90)(87, 89)(92, 130)(93,
129)(94, 128)(95, 136)(98, 141)(100, 123)(110, 163)(111, 127)(116, 119)(117,
118)(120, 138)(121, 137)(122, 153)(124, 158)(125, 156)(133, 164)(134, 148)(139,
152)(140, 151)(146, 149)(147, 165)(150, 162)(154, 159)(155, 160)(157, 161)
c: (4, 5)(6, 8)(7, 10)(9, 13)(11, 16)(12, 18)(14, 19)(15, 21)(17, 24)(20,
28)(22, 31)(23, 33)(25, 34)(26, 36)(29, 41)(30, 43)(32, 46)(35, 50)(37, 53)(38,
55)(40, 56)(42, 59)(44, 62)(45, 64)(47, 65)(48, 67)(51, 71)(52, 73)(54, 76)(57,
80)(58, 82)(60, 83)(61, 85)(63, 88)(66, 92)(68, 95)(69, 96)(72, 99)(74, 102)(75,
104)(77, 105)(78, 107)(79, 91)(81, 109)(84, 113)(86, 116)(87, 117)(89, 118)(90,
119)(93, 122)(94, 123)(98, 127)(100, 128)(101, 130)(103, 132)(106, 136)(108,
131)(110, 139)(111, 141)(112, 135)(114, 144)(115, 145)(120, 138)(121, 148)(124,
149)(125, 151)(126, 143)(129, 153)(133, 155)(134, 137)(140, 156)(146, 158)(147,
159)(150, 161)(152, 163)(154, 165)(157, 162)(160, 164)
C4[ 165, 9 ]
165
-1 12 2 3 18
-2 1 4 5 27
-3 1 6 39 8
-4 2 7 40 9
-5 56 2 13 10
-6 11 57 3 14
-7 12 58 4 15
-8 3 80 16 19
-9 4 81 17 20
-10 5 82 18 21
-11 22 12 6 75
-12 11 1 23 7
-13 24 5 28 109
-14 110 25 6 29
-15 111 26 7 30
-16 104 18 8 31
-17 112 27 9 32
-18 33 1 16 10
-19 34 139 8 41
-20 35 140 9 42
-21 36 141 10 43
-22 11 44 111 37
-23 12 45 38 142
-24 13 46 135 27
-25 143 14 47 39
-26 77 15 48 40
-27 2 24 49 17
-28 13 156 59 50
-29 14 157 60 51
-30 100 15 61 52
-31 16 62 53 141
-32 17 63 97 54
-33 55 18 64 142
-34 126 39 19 65
-35 66 40 118 20
-36 56 67 105 21
-37 22 57 68 54
-38 23 58 69 107
-39 34 3 25 49
-40 35 4 26 70
-41 71 83 19 162
-42 146 72 84 20
-43 73 128 85 21
-44 22 72 74 86
-45 23 75 130 87
-46 88 24 97 76
-47 77 89 25 70
-48 78 90 26 127
-49 79 91 27 39
-50 56 89 92 28
-51 88 57 93 29
-52 144 58 94 30
-53 80 95 31 76
-54 37 81 136 32
-55 33 78 82 96
-56 36 70 5 50
-57 37 6 51 97
-58 38 7 52 98
-59 99 113 158 28
-60 100 114 115 29
-61 101 115 159 30
-62 99 102 116 31
-63 103 71 32 153
-64 33 101 104 117
-65 34 70 105 118
-66 35 114 127 106
-67 36 107 119 98
-68 101 37 151 120
-69 121 38 108 152
-70 56 47 40 65
-71 122 80 41 63
-72 44 81 42 119
-73 123 114 82 43
-74 44 113 124 75
-75 11 45 125 74
-76 46 106 53 109
-77 110 134 47 26
-78 55 111 48 86
-79 112 49 126 108
-80 71 8 53 97
-81 72 9 54 98
-82 55 127 73 10
-83 144 145 128 41
-84 102 93 129 42
-85 145 147 130 43
-86 44 78 146 148
-87 45 147 131 164
-88 132 46 51 129
-89 165 133 47 50
-90 99 134 48 149
-91 143 135 49 131
-92 144 136 50 98
-93 137 51 84 151
-94 145 138 52 152
-95 125 138 53 130
-96 55 148 163 131
-97 46 57 80 32
-98 67 58 81 92
-99 90 59 62 109
-100 110 60 138 30
-101 111 68 61 64
-102 104 149 62 84
-103 112 145 150 63
-104 102 16 151 64
-105 36 137 139 65
-106 66 138 140 76
-107 67 38 116 141
-108 79 69 117 142
-109 99 13 127 76
-110 77 100 14 125
-111 22 78 101 15
-112 79 103 17 152
-113 122 59 74 153
-114 66 154 60 73
-115 132 123 60 61
-116 121 158 62 107
-117 159 160 64 108
-118 154 155 35 65
-119 67 124 137 72
-120 68 123 136 128
-121 69 116 161 129
-122 134 113 125 71
-123 115 73 163 120
-124 158 74 119 164
-125 110 122 95 75
-126 34 155 79 160
-127 66 48 82 109
-128 83 139 43 120
-129 88 121 84 140
-130 45 95 85 141
-131 91 96 87 142
-132 88 135 115 161
-133 143 89 158 161
-134 77 122 90 162
-135 132 24 91 163
-136 156 92 54 120
-137 157 93 105 119
-138 100 94 95 106
-139 105 128 19 151
-140 106 129 20 152
-141 107 31 130 21
-142 33 23 108 131
-143 133 25 91 164
-144 165 92 83 52
-145 103 83 94 85
-146 155 149 42 86
-147 154 150 85 87
-148 150 96 86 153
-149 90 102 146 160
-150 155 103 147 148
-151 68 93 104 139
-152 112 69 94 140
-153 156 113 148 63
-154 157 114 147 118
-155 146 126 150 118
-156 136 28 163 153
-157 154 137 29 164
-158 133 124 59 116
-159 165 61 117 161
-160 126 149 117 162
-161 121 132 133 159
-162 165 134 160 41
-163 123 156 135 96
-164 143 124 157 87
-165 89 144 159 162
0