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