Graph forms
for C4 [ 160, 37 ] = KE_40(1,19,2,23,1)
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On this page are computer-accessible forms for the graph C4[ 160, 37 ] =
KE_40(1,19,2,23,1).
(I) Following is a form readable by MAGMA:
g:=Graph<160|{ {2, 3}, {158, 159}, {156, 157}, {154, 155}, {152, 153}, {150,
151}, {148, 149}, {146, 147}, {144, 145}, {142, 143}, {140, 141}, {138, 139},
{136, 137}, {38, 39}, {36, 37}, {34, 35}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12,
13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {26, 27}, {28,
29}, {30, 31}, {32, 33}, {122, 123}, {124, 125}, {126, 127}, {128, 129}, {130,
131}, {132, 133}, {134, 135}, {80, 82}, {1, 2}, {157, 158}, {153, 154}, {149,
150}, {145, 146}, {141, 142}, {137, 138}, {37, 38}, {5, 6}, {9, 10}, {13, 14},
{17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {121, 122}, {125, 126}, {129,
130}, {133, 134}, {3, 4}, {155, 156}, {147, 148}, {139, 140}, {35, 36}, {11,
12}, {19, 20}, {27, 28}, {123, 124}, {131, 132}, {7, 8}, {151, 152}, {39, 40},
{23, 24}, {135, 136}, {32, 53}, {40, 61}, {34, 55}, {33, 54}, {35, 56}, {39,
60}, {36, 57}, {38, 59}, {79, 81}, {15, 16}, {143, 144}, {37, 58}, {64, 104},
{65, 105}, {66, 106}, {67, 107}, {68, 108}, {69, 109}, {70, 110}, {71, 111},
{80, 120}, {81, 121}, {82, 122}, {83, 123}, {84, 124}, {85, 125}, {86, 126},
{87, 127}, {1, 40}, {64, 106}, {65, 107}, {68, 110}, {69, 111}, {27, 48}, {31,
52}, {28, 49}, {30, 51}, {66, 108}, {67, 109}, {29, 50}, {24, 45}, {26, 47},
{70, 112}, {71, 113}, {78, 120}, {25, 46}, {72, 112}, {73, 113}, {74, 114}, {75,
115}, {76, 116}, {77, 117}, {78, 118}, {79, 119}, {72, 114}, {73, 115}, {76,
118}, {77, 119}, {23, 44}, {2, 63}, {20, 41}, {22, 43}, {74, 116}, {75, 117},
{1, 62}, {159, 160}, {21, 42}, {31, 32}, {64, 127}, {59, 122}, {61, 124}, {63,
126}, {3, 64}, {58, 121}, {7, 68}, {11, 72}, {15, 76}, {19, 80}, {62, 125}, {4,
65}, {6, 67}, {12, 73}, {14, 75}, {5, 66}, {13, 74}, {60, 123}, {8, 69}, {10,
71}, {9, 70}, {1, 81}, {40, 120}, {39, 119}, {38, 118}, {37, 117}, {36, 116},
{35, 115}, {34, 114}, {33, 113}, {2, 82}, {3, 83}, {4, 84}, {5, 85}, {6, 86},
{7, 87}, {8, 88}, {9, 89}, {10, 90}, {11, 91}, {12, 92}, {13, 93}, {14, 94},
{15, 95}, {32, 112}, {54, 96}, {55, 97}, {62, 104}, {63, 105}, {56, 96}, {59,
99}, {58, 98}, {57, 97}, {60, 100}, {61, 101}, {62, 102}, {63, 103}, {56, 98},
{57, 99}, {60, 102}, {61, 103}, {16, 77}, {18, 79}, {58, 100}, {59, 101}, {17,
78}, {48, 88}, {55, 95}, {54, 94}, {53, 93}, {52, 92}, {51, 91}, {50, 90}, {49,
89}, {48, 90}, {53, 95}, {52, 94}, {49, 91}, {50, 92}, {51, 93}, {16, 96}, {17,
97}, {18, 98}, {19, 99}, {20, 100}, {21, 101}, {22, 102}, {23, 103}, {24, 104},
{25, 105}, {26, 106}, {27, 107}, {28, 108}, {29, 109}, {30, 110}, {31, 111},
{46, 88}, {47, 89}, {41, 81}, {47, 87}, {46, 86}, {45, 85}, {44, 84}, {43, 83},
{42, 82}, {41, 83}, {45, 87}, {44, 86}, {42, 84}, {43, 85}, {57, 160}, {48,
151}, {56, 159}, {49, 152}, {55, 158}, {53, 156}, {51, 154}, {50, 153}, {54,
157}, {52, 155}, {41, 144}, {47, 150}, {45, 148}, {43, 146}, {42, 145}, {46,
149}, {44, 147}, {65, 128}, {67, 130}, {69, 132}, {71, 134}, {73, 136}, {75,
138}, {77, 140}, {79, 142}, {66, 129}, {70, 133}, {74, 137}, {78, 141}, {68,
131}, {76, 139}, {72, 135}, {88, 128}, {89, 129}, {90, 130}, {91, 131}, {92,
132}, {93, 133}, {94, 134}, {95, 135}, {120, 160}, {121, 160}, {80, 143}, {96,
136}, {97, 137}, {98, 138}, {99, 139}, {100, 140}, {101, 141}, {102, 142}, {103,
143}, {112, 152}, {113, 153}, {114, 154}, {115, 155}, {116, 156}, {117, 157},
{118, 158}, {119, 159}, {104, 144}, {105, 145}, {106, 146}, {107, 147}, {108,
148}, {109, 149}, {110, 150}, {111, 151}, {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: (2, 40)(3, 39)(4, 38)(5, 37)(6, 36)(7, 35)(8, 34)(9, 33)(10, 32)(11, 31)(12,
30)(13, 29)(14, 28)(15, 27)(16, 26)(17, 25)(18, 24)(19, 23)(20, 22)(41, 102)(42,
101)(43, 100)(44, 99)(45, 98)(46, 97)(47, 96)(48, 95)(49, 94)(50, 93)(51,
92)(52, 91)(53, 90)(54, 89)(55, 88)(56, 87)(57, 86)(58, 85)(59, 84)(60, 83)(61,
82)(62, 81)(63, 120)(64, 119)(65, 118)(66, 117)(67, 116)(68, 115)(69, 114)(70,
113)(71, 112)(72, 111)(73, 110)(74, 109)(75, 108)(76, 107)(77, 106)(78, 105)(79,
104)(80, 103)(121, 125)(122, 124)(126, 160)(127, 159)(128, 158)(129, 157)(130,
156)(131, 155)(132, 154)(133, 153)(134, 152)(135, 151)(136, 150)(137, 149)(138,
148)(139, 147)(140, 146)(141, 145)(142, 144) (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, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40)(41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80)(81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120)(121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160)
c: (2, 62)(3, 125)(4, 85)(6, 66)(7, 129)(8, 89)(10, 70)(11, 133)(12, 93)(14,
74)(15, 137)(16, 97)(18, 78)(19, 141)(20, 101)(22, 42)(23, 145)(24, 105)(26,
46)(27, 149)(28, 109)(30, 50)(31, 153)(32, 113)(34, 54)(35, 157)(36, 117)(38,
58)(39, 121)(40, 81)(41, 61)(43, 84)(44, 146)(45, 65)(47, 88)(48, 150)(49,
69)(51, 92)(52, 154)(53, 73)(55, 96)(56, 158)(57, 77)(59, 100)(60, 122)(63,
104)(64, 126)(67, 108)(68, 130)(71, 112)(72, 134)(75, 116)(76, 138)(79, 120)(80,
142)(82, 102)(83, 124)(86, 106)(87, 128)(90, 110)(91, 132)(94, 114)(95, 136)(98,
118)(99, 140)(103, 144)(107, 148)(111, 152)(115, 156)(119, 160)
C4[ 160, 37 ]
160
-1 2 81 40 62
-2 1 3 82 63
-3 2 4 83 64
-4 3 5 84 65
-5 66 4 6 85
-6 67 5 7 86
-7 68 6 8 87
-8 88 69 7 9
-9 89 70 8 10
-10 11 90 71 9
-11 12 91 72 10
-12 11 13 92 73
-13 12 14 93 74
-14 13 15 94 75
-15 14 16 95 76
-16 77 15 17 96
-17 78 16 18 97
-18 79 17 19 98
-19 99 80 18 20
-20 100 19 41 21
-21 22 101 20 42
-22 23 102 21 43
-23 22 44 24 103
-24 23 45 25 104
-25 24 46 26 105
-26 25 47 27 106
-27 26 48 28 107
-28 27 49 29 108
-29 28 50 30 109
-30 110 29 51 31
-31 111 30 52 32
-32 33 112 31 53
-33 34 113 32 54
-34 33 55 35 114
-35 34 56 36 115
-36 35 57 37 116
-37 36 58 38 117
-38 37 59 39 118
-39 38 60 40 119
-40 1 39 61 120
-41 144 81 83 20
-42 145 82 84 21
-43 22 146 83 85
-44 23 147 84 86
-45 24 148 85 87
-46 88 25 149 86
-47 89 26 150 87
-48 88 90 27 151
-49 89 91 28 152
-50 90 92 29 153
-51 154 91 93 30
-52 155 92 94 31
-53 156 93 95 32
-54 33 157 94 96
-55 34 158 95 97
-56 35 159 96 98
-57 99 36 160 97
-58 121 100 37 98
-59 99 122 101 38
-60 100 123 102 39
-61 101 124 103 40
-62 1 102 125 104
-63 2 103 126 105
-64 3 104 127 106
-65 4 105 128 107
-66 5 106 129 108
-67 6 107 130 109
-68 110 7 108 131
-69 132 111 8 109
-70 110 133 112 9
-71 111 134 113 10
-72 11 112 135 114
-73 12 113 136 115
-74 13 114 137 116
-75 14 115 138 117
-76 15 116 139 118
-77 16 117 140 119
-78 17 118 141 120
-79 81 18 119 142
-80 143 82 19 120
-81 121 1 79 41
-82 122 2 80 42
-83 123 3 41 43
-84 44 124 4 42
-85 45 125 5 43
-86 44 46 126 6
-87 45 47 127 7
-88 46 48 128 8
-89 47 49 129 9
-90 48 50 130 10
-91 11 49 51 131
-92 132 12 50 52
-93 133 13 51 53
-94 134 14 52 54
-95 55 135 15 53
-96 56 136 16 54
-97 55 57 137 17
-98 56 58 138 18
-99 57 59 139 19
-100 58 60 140 20
-101 59 61 141 21
-102 22 60 62 142
-103 143 23 61 63
-104 144 24 62 64
-105 145 25 63 65
-106 66 146 26 64
-107 67 147 27 65
-108 66 68 148 28
-109 67 69 149 29
-110 68 70 150 30
-111 69 71 151 31
-112 70 72 152 32
-113 33 71 73 153
-114 154 34 72 74
-115 155 35 73 75
-116 156 36 74 76
-117 77 157 37 75
-118 78 158 38 76
-119 77 79 159 39
-120 78 80 160 40
-121 122 58 81 160
-122 121 123 59 82
-123 122 124 60 83
-124 123 125 61 84
-125 124 126 62 85
-126 125 127 63 86
-127 126 128 64 87
-128 88 127 129 65
-129 66 89 128 130
-130 67 90 129 131
-131 132 68 91 130
-132 133 69 92 131
-133 132 134 70 93
-134 133 135 71 94
-135 134 136 72 95
-136 135 137 73 96
-137 136 138 74 97
-138 137 139 75 98
-139 99 138 140 76
-140 77 100 139 141
-141 78 101 140 142
-142 143 79 102 141
-143 144 80 103 142
-144 143 145 104 41
-145 144 146 105 42
-146 145 147 106 43
-147 44 146 148 107
-148 45 147 149 108
-149 46 148 150 109
-150 110 47 149 151
-151 111 48 150 152
-152 112 49 151 153
-153 154 113 50 152
-154 155 114 51 153
-155 154 156 115 52
-156 155 157 116 53
-157 156 158 117 54
-158 55 157 159 118
-159 56 158 160 119
-160 121 57 159 120
0