Graph forms
for C4 [ 180, 10 ] = PS(12,15;2)
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On this page are computer-accessible forms for the graph C4[ 180, 10 ] =
PS(12,15;2).
(I) Following is a form readable by MAGMA:
g:=Graph<180|{ {29, 31}, {149, 151}, {89, 91}, {42, 46}, {163, 167}, {162, 166},
{43, 47}, {104, 108}, {105, 109}, {90, 92}, {56, 63}, {75, 76}, {120, 127}, {53,
61}, {55, 63}, {54, 62}, {113, 121}, {114, 122}, {115, 123}, {116, 124}, {117,
125}, {118, 126}, {119, 127}, {55, 62}, {115, 122}, {117, 124}, {119, 126}, {36,
47}, {164, 175}, {160, 171}, {54, 61}, {96, 107}, {100, 111}, {114, 121}, {118,
125}, {102, 106}, {165, 169}, {164, 168}, {103, 107}, {18, 31}, {163, 174},
{161, 172}, {146, 159}, {144, 157}, {80, 93}, {35, 46}, {82, 95}, {97, 108},
{99, 110}, {64, 78}, {150, 152}, {65, 79}, {128, 142}, {129, 143}, {81, 94},
{162, 173}, {145, 158}, {98, 109}, {116, 123}, {135, 136}, {1, 17}, {74, 90},
{73, 89}, {72, 88}, {71, 87}, {70, 86}, {69, 85}, {68, 84}, {67, 83}, {66, 82},
{65, 81}, {64, 80}, {2, 18}, {3, 19}, {4, 20}, {5, 21}, {6, 22}, {7, 23}, {8,
24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14, 30}, {128, 144},
{129, 145}, {130, 146}, {131, 147}, {132, 148}, {133, 149}, {134, 150}, {76,
93}, {142, 159}, {140, 157}, {78, 95}, {136, 153}, {138, 155}, {2, 16}, {75,
89}, {74, 88}, {71, 85}, {70, 84}, {67, 81}, {66, 80}, {3, 17}, {6, 20}, {7,
21}, {10, 24}, {11, 25}, {14, 28}, {15, 29}, {130, 144}, {131, 145}, {134, 148},
{135, 149}, {32, 51}, {160, 179}, {143, 156}, {141, 158}, {79, 92}, {77, 94},
{36, 55}, {40, 59}, {96, 115}, {100, 119}, {137, 154}, {139, 152}, {33, 52},
{165, 176}, {161, 180}, {142, 155}, {140, 153}, {78, 91}, {45, 56}, {35, 54},
{37, 48}, {39, 50}, {41, 60}, {97, 116}, {99, 118}, {101, 112}, {103, 114}, {4,
18}, {69, 83}, {68, 82}, {5, 19}, {12, 26}, {13, 27}, {132, 146}, {133, 147},
{34, 53}, {141, 154}, {139, 156}, {38, 49}, {98, 117}, {102, 113}, {32, 58},
{33, 59}, {40, 51}, {44, 55}, {104, 115}, {44, 48}, {45, 49}, {37, 56}, {43,
54}, {39, 58}, {41, 52}, {101, 120}, {105, 116}, {138, 151}, {8, 22}, {73, 87},
{72, 86}, {9, 23}, {34, 60}, {1, 30}, {42, 53}, {15, 16}, {38, 57}, {76, 104},
{77, 105}, {31, 57}, {151, 177}, {94, 120}, {92, 118}, {153, 179}, {152, 178},
{93, 119}, {136, 164}, {137, 165}, {31, 50}, {159, 178}, {157, 176}, {93, 112},
{95, 114}, {91, 117}, {154, 180}, {79, 96}, {158, 177}, {143, 160}, {94, 113},
{16, 33}, {148, 165}, {146, 163}, {144, 161}, {80, 97}, {18, 35}, {20, 37}, {22,
39}, {24, 41}, {26, 43}, {28, 45}, {82, 99}, {84, 101}, {86, 103}, {88, 105},
{17, 34}, {156, 175}, {152, 171}, {147, 160}, {145, 162}, {81, 98}, {19, 32},
{21, 38}, {23, 36}, {25, 42}, {27, 40}, {83, 96}, {85, 102}, {87, 100}, {92,
111}, {20, 33}, {159, 170}, {157, 168}, {155, 174}, {153, 172}, {150, 163},
{148, 161}, {22, 35}, {28, 41}, {30, 43}, {84, 97}, {86, 99}, {91, 110}, {95,
106}, {19, 36}, {158, 169}, {154, 173}, {149, 162}, {147, 164}, {21, 34}, {27,
44}, {29, 42}, {83, 100}, {85, 98}, {156, 167}, {16, 44}, {17, 45}, {24, 37},
{155, 166}, {151, 170}, {26, 39}, {88, 101}, {90, 103}, {30, 32}, {23, 40}, {25,
38}, {87, 104}, {89, 102}, {61, 90}, {47, 70}, {46, 68}, {47, 69}, {46, 69},
{61, 77}, {63, 79}, {62, 78}, {62, 76}, {63, 77}, {48, 70}, {49, 71}, {48, 71},
{56, 64}, {60, 68}, {59, 67}, {58, 66}, {57, 65}, {49, 72}, {59, 66}, {57, 64},
{51, 74}, {50, 72}, {51, 73}, {50, 73}, {58, 65}, {52, 74}, {53, 75}, {52, 75},
{60, 67}, {10, 168}, {11, 169}, {14, 172}, {15, 173}, {11, 168}, {15, 172}, {12,
169}, {14, 171}, {12, 170}, {13, 171}, {13, 170}, {1, 173}, {2, 174}, {3, 175},
{2, 175}, {10, 167}, {8, 166}, {9, 167}, {1, 174}, {9, 166}, {3, 176}, {7, 180},
{4, 176}, {5, 177}, {6, 178}, {7, 179}, {4, 177}, {6, 179}, {5, 178}, {8, 180},
{107, 130}, {109, 132}, {111, 134}, {106, 128}, {107, 129}, {110, 132}, {111,
133}, {106, 129}, {110, 133}, {108, 130}, {109, 131}, {108, 131}, {121, 150},
{121, 137}, {122, 138}, {123, 139}, {124, 140}, {125, 141}, {126, 142}, {127,
143}, {122, 136}, {123, 137}, {126, 140}, {127, 141}, {112, 134}, {113, 135},
{124, 138}, {125, 139}, {112, 135}, {120, 128} }>;
(II) A more general form is to represent the graph as the orbit of {29, 31}
under the group generated by the following permutations:
a: (2, 15)(3, 14)(4, 13)(5, 12)(6, 11)(7, 10)(8, 9)(17, 30)(18, 29)(19, 28)(20,
27)(21, 26)(22, 25)(23, 24)(32, 45)(33, 44)(34, 43)(35, 42)(36, 41)(37, 40)(38,
39)(47, 60)(48, 59)(49, 58)(50, 57)(51, 56)(52, 55)(53, 54)(62, 75)(63, 74)(64,
73)(65, 72)(66, 71)(67, 70)(68, 69)(77, 90)(78, 89)(79, 88)(80, 87)(81, 86)(82,
85)(83, 84)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(107,
120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)(122, 135)(123,
134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)(137, 150)(138, 149)(139,
148)(140, 147)(141, 146)(142, 145)(143, 144)(152, 165)(153, 164)(154, 163)(155,
162)(156, 161)(157, 160)(158, 159)(167, 180)(168, 179)(169, 178)(170, 177)(171,
176)(172, 175)(173, 174) (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, 16, 31, 46, 61, 76, 91, 106, 121, 136, 151, 166)(2, 18, 35, 54, 62, 78,
95, 114, 122, 138, 155, 174)(3, 20, 39, 47, 63, 80, 99, 107, 123, 140, 159,
167)(4, 22, 43, 55, 64, 82, 103, 115, 124, 142, 163, 175)(5, 24, 32, 48, 65, 84,
92, 108, 125, 144, 152, 168)(6, 26, 36, 56, 66, 86, 96, 116, 126, 146, 156,
176)(7, 28, 40, 49, 67, 88, 100, 109, 127, 148, 160, 169)(8, 30, 44, 57, 68, 90,
104, 117, 128, 150, 164, 177)(9, 17, 33, 50, 69, 77, 93, 110, 129, 137, 153,
170)(10, 19, 37, 58, 70, 79, 97, 118, 130, 139, 157, 178)(11, 21, 41, 51, 71,
81, 101, 111, 131, 141, 161, 171)(12, 23, 45, 59, 72, 83, 105, 119, 132, 143,
165, 179)(13, 25, 34, 52, 73, 85, 94, 112, 133, 145, 154, 172)(14, 27, 38, 60,
74, 87, 98, 120, 134, 147, 158, 180)(15, 29, 42, 53, 75, 89, 102, 113, 135, 149,
162, 173)
c: (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, 161, 162, 163, 164,
165)(166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179,
180)
C4[ 180, 10 ]
180
-1 17 30 173 174
-2 16 18 174 175
-3 176 17 19 175
-4 176 177 18 20
-5 177 178 19 21
-6 22 178 179 20
-7 23 179 180 21
-8 22 166 24 180
-9 23 166 167 25
-10 24 167 168 26
-11 25 168 169 27
-12 26 169 170 28
-13 27 170 171 29
-14 28 171 172 30
-15 16 29 172 173
-16 33 44 2 15
-17 1 34 45 3
-18 2 35 4 31
-19 3 36 5 32
-20 33 4 37 6
-21 34 5 38 7
-22 35 6 39 8
-23 36 7 40 9
-24 37 8 41 10
-25 11 38 9 42
-26 12 39 10 43
-27 11 44 13 40
-28 12 45 14 41
-29 13 15 31 42
-30 1 14 32 43
-31 57 50 18 29
-32 58 51 19 30
-33 59 16 52 20
-34 60 17 53 21
-35 22 46 18 54
-36 55 23 47 19
-37 56 24 48 20
-38 57 25 49 21
-39 22 58 26 50
-40 23 59 27 51
-41 24 60 28 52
-42 46 25 29 53
-43 47 26 30 54
-44 55 48 16 27
-45 56 49 17 28
-46 35 68 69 42
-47 36 69 70 43
-48 44 37 70 71
-49 45 38 71 72
-50 39 72 73 31
-51 40 73 74 32
-52 33 41 74 75
-53 34 61 42 75
-54 35 61 62 43
-55 44 36 62 63
-56 45 37 63 64
-57 38 31 64 65
-58 66 39 32 65
-59 33 66 67 40
-60 34 67 68 41
-61 77 90 53 54
-62 55 78 54 76
-63 55 77 56 79
-64 56 78 57 80
-65 57 79 58 81
-66 58 80 59 82
-67 59 81 60 83
-68 46 60 82 84
-69 46 47 83 85
-70 47 48 84 86
-71 48 49 85 87
-72 88 49 50 86
-73 89 50 51 87
-74 88 90 51 52
-75 89 52 53 76
-76 93 104 62 75
-77 61 94 105 63
-78 91 62 95 64
-79 92 63 96 65
-80 66 93 64 97
-81 67 94 65 98
-82 66 99 68 95
-83 67 100 69 96
-84 68 101 70 97
-85 69 102 71 98
-86 99 70 103 72
-87 100 71 104 73
-88 101 72 105 74
-89 91 102 73 75
-90 92 103 61 74
-91 110 78 89 117
-92 111 79 90 118
-93 112 80 119 76
-94 77 113 81 120
-95 78 114 82 106
-96 79 115 83 107
-97 80 116 84 108
-98 81 117 85 109
-99 110 82 118 86
-100 111 83 119 87
-101 88 112 84 120
-102 89 113 106 85
-103 90 114 107 86
-104 115 108 76 87
-105 77 88 116 109
-106 102 95 128 129
-107 103 96 129 130
-108 104 97 130 131
-109 132 105 98 131
-110 99 132 133 91
-111 100 133 134 92
-112 101 134 135 93
-113 121 102 135 94
-114 121 122 103 95
-115 122 123 104 96
-116 123 124 105 97
-117 91 124 125 98
-118 99 92 125 126
-119 100 93 126 127
-120 101 94 127 128
-121 113 114 137 150
-122 114 136 115 138
-123 115 137 116 139
-124 116 138 117 140
-125 117 139 118 141
-126 118 140 119 142
-127 143 119 141 120
-128 144 106 120 142
-129 143 145 106 107
-130 144 146 107 108
-131 145 147 108 109
-132 110 146 148 109
-133 110 111 147 149
-134 111 112 148 150
-135 112 113 136 149
-136 122 135 153 164
-137 121 154 165 123
-138 122 155 124 151
-139 123 156 125 152
-140 124 157 126 153
-141 154 125 158 127
-142 155 126 159 128
-143 156 127 160 129
-144 157 128 161 130
-145 158 129 162 131
-146 132 159 130 163
-147 133 160 131 164
-148 132 165 134 161
-149 133 135 151 162
-150 121 134 152 163
-151 177 170 138 149
-152 178 171 139 150
-153 179 136 172 140
-154 180 137 173 141
-155 166 138 174 142
-156 143 167 139 175
-157 176 144 168 140
-158 177 145 169 141
-159 178 146 170 142
-160 143 179 147 171
-161 144 180 148 172
-162 166 145 149 173
-163 167 146 150 174
-164 168 136 147 175
-165 176 169 137 148
-166 155 8 162 9
-167 156 9 163 10
-168 11 157 10 164
-169 11 165 12 158
-170 12 13 159 151
-171 13 14 160 152
-172 14 15 161 153
-173 154 1 15 162
-174 1 155 2 163
-175 2 156 3 164
-176 165 3 157 4
-177 4 158 5 151
-178 5 159 6 152
-179 6 160 7 153
-180 154 7 161 8
0