Graph forms
for C4 [ 165, 10 ] = L(F110)
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On this page are computer-accessible forms for the graph C4[ 165, 10 ] =
L(F110).
(I) Following is a form readable by MAGMA:
g:=Graph<165|{ {2, 3}, {164, 165}, {160, 161}, {158, 159}, {154, 155}, {152,
153}, {148, 149}, {146, 147}, {142, 143}, {140, 141}, {136, 137}, {118, 119},
{116, 117}, {110, 111}, {108, 109}, {4, 5}, {56, 57}, {58, 59}, {60, 61}, {62,
63}, {76, 77}, {78, 79}, {80, 81}, {82, 83}, {86, 87}, {88, 89}, {94, 95}, {1,
3}, {160, 162}, {157, 159}, {148, 150}, {145, 147}, {136, 138}, {93, 95}, {1,
2}, {161, 162}, {157, 158}, {149, 150}, {145, 146}, {137, 138}, {133, 134},
{129, 130}, {125, 126}, {121, 122}, {113, 114}, {105, 106}, {101, 102}, {97,
98}, {49, 50}, {53, 54}, {65, 66}, {69, 70}, {1, 5}, {25, 29}, {24, 28}, {17,
21}, {16, 20}, {3, 7}, {2, 6}, {89, 93}, {1, 4}, {10, 12}, {163, 165}, {154,
156}, {139, 141}, {11, 13}, {51, 52}, {163, 164}, {155, 156}, {139, 140}, {131,
132}, {123, 124}, {99, 100}, {67, 68}, {4, 12}, {130, 138}, {37, 45}, {36, 44},
{35, 43}, {34, 42}, {33, 41}, {32, 40}, {7, 15}, {6, 14}, {5, 13}, {132, 141},
{146, 155}, {2, 8}, {3, 9}, {129, 138}, {22, 26}, {147, 159}, {114, 126}, {23,
27}, {100, 105}, {4, 10}, {151, 153}, {148, 154}, {131, 141}, {7, 9}, {6, 8},
{5, 11}, {71, 72}, {151, 152}, {103, 104}, {10, 26}, {128, 144}, {15, 31}, {14,
30}, {13, 29}, {12, 28}, {11, 27}, {44, 61}, {135, 150}, {106, 123}, {47, 62},
{46, 60}, {99, 113}, {66, 80}, {74, 88}, {6, 18}, {13, 25}, {12, 24}, {7, 19},
{33, 52}, {37, 48}, {78, 91}, {68, 83}, {137, 158}, {8, 16}, {9, 17}, {36, 63},
{111, 116}, {41, 50}, {79, 84}, {8, 20}, {15, 19}, {14, 18}, {11, 23}, {10, 22},
{9, 21}, {70, 90}, {43, 54}, {39, 57}, {142, 144}, {72, 86}, {47, 48}, {143,
144}, {133, 165}, {134, 165}, {28, 56}, {31, 59}, {64, 100}, {91, 126}, {135,
162}, {73, 111}, {90, 124}, {29, 58}, {14, 38}, {136, 160}, {15, 39}, {69, 109},
{81, 121}, {85, 125}, {23, 62}, {24, 49}, {64, 105}, {66, 107}, {80, 121}, {91,
114}, {22, 60}, {25, 51}, {65, 107}, {67, 104}, {70, 109}, {92, 119}, {27, 55},
{68, 104}, {86, 122}, {87, 122}, {26, 53}, {84, 123}, {16, 32}, {94, 110}, {21,
37}, {20, 36}, {19, 35}, {18, 34}, {17, 33}, {79, 127}, {78, 127}, {71, 115},
{150, 162}, {76, 120}, {77, 120}, {16, 40}, {31, 39}, {30, 38}, {23, 47}, {22,
46}, {21, 45}, {20, 44}, {19, 43}, {18, 42}, {17, 41}, {72, 115}, {73, 116},
{75, 118}, {84, 106}, {74, 117}, {46, 110}, {53, 112}, {30, 88}, {54, 112}, {55,
113}, {47, 96}, {48, 96}, {60, 108}, {61, 108}, {51, 97}, {29, 73}, {49, 101},
{31, 75}, {30, 74}, {55, 99}, {52, 97}, {50, 101}, {24, 64}, {25, 65}, {63,
103}, {26, 67}, {62, 103}, {56, 98}, {28, 71}, {57, 98}, {58, 102}, {59, 102},
{27, 69}, {48, 81}, {54, 87}, {61, 92}, {32, 66}, {34, 70}, {40, 79}, {50, 85},
{36, 77}, {57, 82}, {33, 76}, {35, 78}, {38, 72}, {42, 68}, {32, 80}, {46, 94},
{45, 93}, {44, 92}, {38, 86}, {59, 75}, {49, 64}, {51, 65}, {55, 69}, {63, 77},
{58, 73}, {37, 81}, {45, 89}, {39, 82}, {53, 67}, {34, 90}, {52, 76}, {35, 91},
{42, 83}, {40, 84}, {43, 87}, {41, 85}, {56, 71}, {96, 160}, {95, 157}, {94,
157}, {103, 163}, {74, 131}, {104, 163}, {75, 133}, {83, 135}, {117, 161}, {85,
129}, {82, 135}, {116, 161}, {88, 128}, {90, 130}, {92, 132}, {89, 128}, {125,
164}, {95, 134}, {126, 164}, {93, 134}, {121, 153}, {109, 143}, {112, 146},
{108, 143}, {122, 153}, {113, 149}, {114, 149}, {120, 159}, {96, 136}, {102,
142}, {98, 139}, {97, 139}, {118, 156}, {101, 142}, {120, 147}, {119, 156},
{112, 155}, {115, 158}, {127, 144}, {124, 140}, {107, 154}, {100, 151}, {119,
132}, {118, 133}, {99, 151}, {110, 152}, {117, 131}, {111, 152}, {123, 140},
{105, 145}, {115, 137}, {106, 145}, {125, 129}, {124, 130}, {107, 148}, {127,
128} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (1, 2)(4, 8)(5, 6)(7, 9)(10, 20)(11, 18)(12, 16)(13, 14)(15, 21)(17, 19)(22,
44)(23, 42)(24, 40)(25, 38)(26, 36)(27, 34)(28, 32)(29, 30)(31, 45)(33, 43)(35,
41)(37, 39)(46, 92)(47, 83)(48, 82)(49, 79)(50, 78)(51, 86)(52, 87)(53, 77)(54,
76)(55, 90)(56, 80)(57, 81)(58, 88)(59, 89)(60, 61)(62, 68)(63, 67)(64, 84)(65,
72)(66, 71)(69, 70)(73, 74)(75, 93)(85, 91)(94, 119)(95, 118)(96, 135)(97,
122)(98, 121)(99, 124)(100, 123)(101, 127)(102, 128)(103, 104)(105, 106)(107,
115)(110, 132)(111, 131)(112, 120)(113, 130)(114, 129)(116, 117)(125, 126)(133,
134)(136, 150)(137, 148)(138, 149)(139, 153)(140, 151)(141, 152)(142, 144)(146,
147)(154, 158)(155, 159)(156, 157)(160, 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: (2, 3)(4, 5)(6, 9)(7, 8)(10, 13)(11, 12)(14, 21)(15, 20)(16, 19)(17, 18)(22,
29)(23, 28)(24, 27)(25, 26)(30, 45)(31, 44)(32, 43)(33, 42)(34, 41)(35, 40)(36,
39)(37, 38)(46, 73)(47, 71)(48, 72)(49, 69)(50, 70)(51, 67)(52, 68)(53, 65)(54,
66)(55, 64)(56, 62)(57, 63)(58, 60)(59, 61)(74, 93)(75, 92)(76, 83)(77, 82)(78,
79)(80, 87)(81, 86)(84, 91)(85, 90)(88, 89)(94, 116)(95, 117)(96, 115)(97,
104)(98, 103)(99, 100)(101, 109)(102, 108)(105, 113)(106, 114)(107, 112)(110,
111)(118, 119)(120, 135)(121, 122)(123, 126)(124, 125)(129, 130)(131, 134)(132,
133)(136, 137)(139, 163)(140, 164)(141, 165)(142, 143)(145, 149)(146, 148)(147,
150)(154, 155)(157, 161)(158, 160)(159, 162)
c: (2, 4)(3, 5)(6, 10)(7, 11)(8, 12)(9, 13)(14, 22)(15, 23)(16, 24)(17, 25)(18,
26)(19, 27)(20, 28)(21, 29)(30, 46)(31, 47)(32, 49)(33, 51)(34, 53)(35, 55)(36,
56)(37, 58)(38, 60)(39, 62)(40, 64)(41, 65)(42, 67)(43, 69)(44, 71)(45, 73)(48,
59)(50, 66)(54, 70)(57, 63)(61, 72)(74, 94)(75, 96)(76, 97)(77, 98)(78, 99)(79,
100)(80, 101)(81, 102)(82, 103)(83, 104)(84, 105)(85, 107)(86, 108)(87, 109)(88,
110)(89, 111)(90, 112)(91, 113)(92, 115)(93, 116)(95, 117)(118, 136)(119,
137)(120, 139)(121, 142)(122, 143)(123, 145)(124, 146)(125, 148)(126, 149)(127,
151)(128, 152)(129, 154)(130, 155)(131, 157)(132, 158)(133, 160)(134, 161)(135,
163)(138, 156)(140, 147)(141, 159)(144, 153)(150, 164)(162, 165)
d: (4, 5)(6, 8)(7, 9)(10, 11)(12, 13)(14, 16)(15, 17)(18, 20)(19, 21)(22,
27)(23, 26)(24, 29)(25, 28)(30, 40)(31, 41)(32, 38)(33, 39)(34, 44)(35, 45)(36,
42)(37, 43)(46, 55)(47, 53)(48, 54)(49, 58)(50, 59)(51, 56)(52, 57)(60, 69)(61,
70)(62, 67)(63, 68)(64, 73)(65, 71)(66, 72)(74, 84)(75, 85)(76, 82)(77, 83)(78,
89)(79, 88)(80, 86)(81, 87)(90, 92)(91, 93)(94, 113)(95, 114)(96, 112)(97,
98)(99, 110)(100, 111)(101, 102)(103, 104)(105, 116)(106, 117)(107, 115)(108,
109)(118, 129)(119, 130)(120, 135)(121, 122)(123, 131)(124, 132)(125, 133)(126,
134)(127, 128)(136, 155)(137, 154)(138, 156)(140, 141)(145, 161)(146, 160)(147,
162)(148, 158)(149, 157)(150, 159)(151, 152)(164, 165)
C4[ 165, 10 ]
165
-1 2 3 4 5
-2 1 3 6 8
-3 1 2 7 9
-4 1 12 5 10
-5 11 1 13 4
-6 2 14 18 8
-7 3 15 19 9
-8 2 16 6 20
-9 3 17 7 21
-10 22 12 4 26
-11 23 13 5 27
-12 24 4 28 10
-13 11 25 5 29
-14 38 6 18 30
-15 39 7 19 31
-16 40 8 20 32
-17 33 41 9 21
-18 34 14 6 42
-19 35 15 7 43
-20 44 36 16 8
-21 45 37 17 9
-22 46 26 60 10
-23 11 47 27 62
-24 12 49 28 64
-25 13 29 51 65
-26 22 67 53 10
-27 11 55 23 69
-28 12 56 24 71
-29 13 25 58 73
-30 88 14 38 74
-31 15 59 39 75
-32 66 80 16 40
-33 17 41 52 76
-34 90 70 18 42
-35 78 91 19 43
-36 44 77 63 20
-37 45 48 81 21
-38 14 72 30 86
-39 57 15 82 31
-40 79 16 84 32
-41 33 17 50 85
-42 34 68 83 18
-43 35 19 54 87
-44 36 92 61 20
-45 89 37 93 21
-46 22 110 60 94
-47 23 48 62 96
-48 47 37 81 96
-49 24 101 50 64
-50 101 49 41 85
-51 25 52 97 65
-52 33 51 97 76
-53 67 112 26 54
-54 112 53 43 87
-55 99 69 113 27
-56 57 71 28 98
-57 56 82 39 98
-58 102 59 29 73
-59 58 102 31 75
-60 22 46 61 108
-61 44 92 60 108
-62 23 47 103 63
-63 77 36 103 62
-64 100 24 49 105
-65 66 25 51 107
-66 80 107 32 65
-67 68 26 104 53
-68 67 104 83 42
-69 55 70 27 109
-70 34 90 69 109
-71 56 115 28 72
-72 38 71 115 86
-73 111 58 116 29
-74 88 117 30 131
-75 133 59 118 31
-76 33 77 52 120
-77 36 63 76 120
-78 35 79 91 127
-79 78 127 40 84
-80 66 121 81 32
-81 121 80 37 48
-82 57 135 39 83
-83 68 135 82 42
-84 79 123 40 106
-85 125 50 41 129
-86 122 38 72 87
-87 122 86 43 54
-88 89 128 30 74
-89 88 45 93 128
-90 34 124 70 130
-91 78 35 114 126
-92 44 132 61 119
-93 45 89 134 95
-94 110 46 157 95
-95 134 157 93 94
-96 47 48 136 160
-97 51 139 52 98
-98 56 57 139 97
-99 55 100 113 151
-100 99 105 151 64
-101 102 49 50 142
-102 101 58 59 142
-103 104 62 63 163
-104 67 68 103 163
-105 100 145 106 64
-106 123 145 105 84
-107 66 154 148 65
-108 143 60 61 109
-109 143 69 70 108
-110 111 46 94 152
-111 110 116 73 152
-112 155 146 53 54
-113 55 99 114 149
-114 91 113 126 149
-115 158 71 137 72
-116 111 73 117 161
-117 116 161 74 131
-118 133 156 75 119
-119 132 156 92 118
-120 77 147 159 76
-121 122 80 81 153
-122 121 86 87 153
-123 124 84 106 140
-124 90 123 140 130
-125 126 85 129 164
-126 91 114 125 164
-127 78 144 79 128
-128 88 89 144 127
-129 125 138 85 130
-130 90 124 138 129
-131 132 117 74 141
-132 92 119 141 131
-133 165 134 118 75
-134 165 133 93 95
-135 82 83 150 162
-136 137 138 160 96
-137 136 158 115 138
-138 136 137 129 130
-139 140 97 141 98
-140 123 124 139 141
-141 132 139 140 131
-142 143 144 101 102
-143 144 108 109 142
-144 143 127 128 142
-145 146 147 105 106
-146 155 112 145 147
-147 145 146 159 120
-148 154 149 150 107
-149 113 114 148 150
-150 135 148 149 162
-151 99 100 152 153
-152 110 111 151 153
-153 121 122 151 152
-154 155 156 148 107
-155 154 112 156 146
-156 154 155 118 119
-157 158 159 94 95
-158 157 115 137 159
-159 157 147 158 120
-160 136 161 96 162
-161 116 160 117 162
-162 135 160 150 161
-163 165 103 104 164
-164 165 125 126 163
-165 133 134 163 164
0