Graph forms
for C4 [ 192, 181 ] = SS[192,66]
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On this page are computer-accessible forms for the graph C4[ 192, 181 ] =
SS[192,66].
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {1, 3}, {1, 2}, {180, 183}, {1, 5}, {178, 182}, {177, 181}, {1,
4}, {144, 153}, {84, 94}, {144, 154}, {85, 95}, {144, 155}, {179, 184}, {176,
187}, {144, 156}, {80, 93}, {81, 92}, {139, 155}, {170, 186}, {169, 185}, {166,
182}, {165, 181}, {143, 159}, {132, 149}, {143, 158}, {136, 153}, {36, 54},
{143, 157}, {133, 151}, {134, 148}, {74, 89}, {175, 188}, {75, 88}, {128, 147},
{129, 146}, {137, 154}, {78, 90}, {174, 186}, {173, 185}, {79, 91}, {130, 150},
{135, 147}, {34, 55}, {141, 152}, {135, 146}, {136, 157}, {138, 159}, {139,
158}, {138, 156}, {134, 145}, {172, 187}, {171, 188}, {160, 183}, {35, 59},
{141, 149}, {36, 61}, {140, 150}, {35, 56}, {164, 191}, {36, 63}, {76, 87}, {77,
86}, {131, 152}, {140, 151}, {34, 62}, {162, 190}, {161, 189}, {37, 57}, {34,
60}, {64, 94}, {65, 95}, {33, 62}, {168, 183}, {167, 184}, {37, 58}, {20, 52},
{31, 63}, {29, 61}, {28, 60}, {27, 59}, {26, 58}, {21, 53}, {132, 166}, {153,
187}, {133, 167}, {18, 49}, {154, 185}, {19, 48}, {71, 100}, {28, 56}, {29, 57},
{70, 99}, {66, 100}, {156, 186}, {67, 101}, {131, 165}, {14, 41}, {159, 184},
{155, 188}, {152, 191}, {21, 50}, {20, 51}, {15, 40}, {68, 99}, {69, 98}, {149,
189}, {158, 182}, {157, 181}, {150, 190}, {14, 39}, {15, 38}, {137, 160}, {130,
168}, {142, 164}, {73, 98}, {148, 191}, {26, 54}, {146, 190}, {145, 189}, {142,
162}, {27, 55}, {72, 101}, {142, 163}, {142, 161}, {143, 160}, {68, 116}, {69,
116}, {64, 114}, {129, 179}, {65, 114}, {82, 97}, {83, 96}, {128, 180}, {67,
117}, {66, 117}, {17, 43}, {17, 42}, {16, 44}, {16, 45}, {19, 46}, {18, 47},
{18, 80}, {18, 81}, {43, 104}, {22, 85}, {23, 83}, {40, 109}, {44, 105}, {41,
108}, {23, 81}, {46, 105}, {47, 103}, {25, 80}, {26, 80}, {27, 81}, {59, 113},
{25, 82}, {45, 102}, {31, 84}, {58, 113}, {24, 84}, {60, 112}, {63, 115}, {30,
83}, {49, 124}, {48, 125}, {42, 103}, {39, 106}, {38, 107}, {61, 112}, {62,
115}, {42, 100}, {43, 101}, {44, 99}, {46, 97}, {45, 98}, {26, 74}, {48, 96},
{27, 75}, {28, 77}, {29, 76}, {20, 70}, {29, 79}, {28, 78}, {23, 69}, {21, 71},
{24, 75}, {147, 192}, {22, 66}, {45, 121}, {44, 120}, {25, 76}, {47, 122}, {46,
123}, {24, 78}, {48, 102}, {56, 110}, {40, 127}, {151, 192}, {57, 110}, {30,
70}, {51, 107}, {50, 106}, {38, 126}, {31, 71}, {55, 111}, {22, 79}, {54, 111},
{53, 108}, {52, 109}, {49, 104}, {14, 84}, {23, 77}, {16, 74}, {14, 85}, {31,
68}, {24, 67}, {16, 75}, {15, 83}, {43, 119}, {42, 118}, {30, 66}, {22, 74},
{19, 79}, {17, 77}, {15, 82}, {25, 68}, {21, 72}, {20, 73}, {19, 78}, {17, 76},
{30, 64}, {62, 97}, {63, 96}, {54, 86}, {55, 87}, {58, 90}, {59, 91}, {32, 65},
{56, 89}, {57, 88}, {60, 93}, {61, 92}, {35, 65}, {32, 67}, {163, 192}, {33,
69}, {35, 71}, {34, 70}, {37, 64}, {51, 91}, {53, 93}, {32, 73}, {33, 72}, {36,
73}, {37, 72}, {50, 92}, {52, 90}, {49, 94}, {39, 87}, {47, 95}, {40, 89}, {9,
123}, {32, 82}, {13, 127}, {11, 120}, {8, 124}, {33, 85}, {13, 121}, {11, 126},
{7, 125}, {12, 118}, {6, 122}, {10, 119}, {38, 88}, {41, 86}, {6, 134}, {9,
137}, {7, 135}, {11, 138}, {13, 140}, {12, 141}, {10, 136}, {7, 132}, {8, 139},
{6, 130}, {13, 137}, {10, 141}, {12, 139}, {11, 140}, {9, 131}, {10, 129}, {12,
128}, {7, 138}, {8, 133}, {6, 136}, {9, 135}, {8, 134}, {39, 129}, {41, 128},
{51, 131}, {52, 132}, {5, 182}, {3, 183}, {2, 181}, {53, 130}, {50, 133}, {3,
186}, {4, 191}, {5, 190}, {4, 184}, {4, 185}, {2, 188}, {5, 187}, {3, 189},
{113, 176}, {117, 180}, {2, 192}, {110, 172}, {102, 162}, {110, 171}, {111,
170}, {116, 177}, {103, 161}, {111, 169}, {116, 178}, {117, 179}, {99, 171},
{104, 160}, {108, 164}, {120, 176}, {107, 162}, {105, 163}, {106, 161}, {101,
169}, {104, 164}, {127, 178}, {97, 175}, {98, 172}, {100, 170}, {109, 163},
{126, 177}, {96, 176}, {122, 169}, {114, 167}, {115, 166}, {115, 165}, {121,
175}, {124, 170}, {125, 171}, {123, 172}, {119, 174}, {114, 168}, {118, 173},
{112, 173}, {112, 174}, {113, 175}, {118, 150}, {119, 151}, {120, 152}, {92,
180}, {91, 178}, {122, 147}, {125, 148}, {123, 145}, {90, 177}, {127, 148},
{121, 149}, {93, 179}, {124, 146}, {126, 145}, {106, 154}, {107, 155}, {108,
156}, {86, 167}, {95, 174}, {94, 173}, {109, 153}, {105, 158}, {103, 159}, {102,
157}, {89, 165}, {88, 166}, {87, 168} }>;
(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: (1, 18, 20, 140, 14, 110, 143, 111, 15, 141, 21, 19)(2, 49, 73, 11, 39, 56,
158, 169, 83, 149, 53, 79)(3, 80, 51, 151, 84, 172, 159, 55, 40, 12, 72, 48)(4,
81, 52, 150, 85, 171, 160, 54, 38, 10, 71, 46)(5, 47, 70, 13, 41, 57, 157, 170,
82, 152, 50, 78)(6, 66, 175, 164, 61, 177, 146, 65, 44, 154, 77, 166)(7, 168,
74, 155, 43, 63, 145, 179, 59, 163, 173, 69)(8, 67, 176, 161, 60, 178, 147, 64,
45, 156, 76, 165)(9, 167, 75, 153, 42, 62, 148, 180, 58, 162, 174, 68)(16, 144,
17, 115, 134, 117, 113, 142, 112, 116, 135, 114)(22, 188, 104, 36, 126, 129, 35,
105, 185, 23, 132, 130)(24, 187, 103, 34, 127, 128, 37, 102, 186, 25, 131,
133)(26, 107, 119, 31, 123, 184, 27, 109, 118, 33, 125, 183)(28, 182, 122, 30,
121, 108, 29, 181, 124, 32, 120, 106)(86, 88, 136, 100, 97, 191, 92, 90, 190,
95, 99, 137)(87, 89, 139, 101, 96, 189, 93, 91, 192, 94, 98, 138) (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, 26)(2, 58)(3, 80)(4, 54)(5, 74)(6, 65)(7, 70)(8, 67)(9, 83)(10, 71)(11,
62)(12, 84)(13, 69)(14, 118)(15, 123)(16, 182)(17, 106)(18, 183)(19, 107)(20,
125)(21, 119)(22, 190)(23, 137)(24, 139)(25, 189)(27, 143)(28, 144)(29, 142)(30,
135)(31, 141)(32, 134)(33, 140)(34, 138)(35, 136)(36, 191)(37, 192)(38, 46)(39,
42)(40, 172)(41, 173)(43, 50)(44, 166)(45, 178)(47, 168)(48, 51)(49, 180)(52,
171)(53, 174)(55, 159)(56, 153)(57, 163)(59, 157)(60, 156)(61, 164)(63, 152)(64,
147)(66, 146)(68, 149)(72, 151)(73, 148)(75, 158)(76, 161)(77, 154)(78, 155)(79,
162)(81, 160)(82, 145)(85, 150)(86, 185)(87, 103)(88, 105)(89, 187)(90, 188)(91,
102)(92, 104)(93, 186)(94, 128)(95, 130)(96, 131)(97, 126)(98, 127)(99,
132)(100, 129)(101, 133)(108, 112)(109, 110)(111, 184)(113, 181)(114, 122)(115,
120)(116, 121)(117, 124)(165, 176)(167, 169)(170, 179)(175, 177)
c: (2, 4)(3, 5)(6, 7)(8, 9)(10, 11)(12, 13)(14, 15)(16, 17)(18, 19)(20, 21)(22,
23)(24, 25)(26, 28)(27, 29)(30, 33)(31, 32)(34, 37)(35, 36)(38, 39)(40, 41)(42,
45)(43, 44)(46, 49)(47, 48)(50, 51)(52, 53)(54, 56)(55, 57)(58, 60)(59, 61)(62,
64)(63, 65)(66, 69)(67, 68)(70, 72)(71, 73)(74, 77)(75, 76)(78, 80)(79, 81)(82,
84)(83, 85)(86, 89)(87, 88)(90, 93)(91, 92)(94, 97)(95, 96)(98, 100)(99,
101)(102, 103)(104, 105)(106, 107)(108, 109)(110, 111)(112, 113)(114, 115)(116,
117)(118, 121)(119, 120)(122, 125)(123, 124)(126, 129)(127, 128)(130, 132)(131,
133)(134, 135)(136, 138)(137, 139)(140, 141)(145, 146)(147, 148)(149, 150)(151,
152)(153, 156)(154, 155)(157, 159)(158, 160)(161, 162)(163, 164)(165, 167)(166,
168)(169, 171)(170, 172)(173, 175)(174, 176)(177, 179)(178, 180)(181, 184)(182,
183)(185, 188)(186, 187)(189, 190)(191, 192)
d: (1, 22, 140, 34, 143, 35, 141, 25)(2, 66, 13, 60, 158, 65, 152, 76)(3, 74,
150, 62, 159, 59, 10, 68)(4, 79, 151, 70, 160, 56, 12, 82)(5, 85, 11, 55, 157,
71, 149, 80)(6, 63, 161, 58, 146, 69, 156, 75)(7, 81, 153, 84, 145, 54, 162,
72)(8, 73, 164, 57, 147, 83, 154, 78)(9, 77, 155, 67, 148, 61, 163, 64)(14, 126,
111, 102, 21, 132, 18, 187)(15, 185, 19, 133, 20, 104, 110, 128)(16, 130, 115,
103, 113, 129, 116, 186)(17, 188, 117, 127, 112, 105, 114, 131)(23, 144, 24,
134, 36, 142, 37, 135)(26, 190, 33, 138, 27, 136, 31, 189)(28, 139, 32, 191, 29,
192, 30, 137)(38, 169, 48, 50, 52, 49, 172, 41)(39, 177, 170, 45, 53, 166, 47,
176)(40, 173, 46, 167, 51, 43, 171, 180)(42, 175, 179, 178, 174, 44, 168,
165)(86, 107, 101, 125, 92, 109, 94, 123)(87, 181, 100, 121, 93, 182, 95,
120)(88, 122, 96, 106, 90, 124, 98, 108)(89, 118, 97, 184, 91, 119, 99, 183)
e: (2, 5)(3, 4)(6, 8)(7, 9)(10, 12)(11, 13)(22, 24)(23, 25)(26, 27)(28, 29)(30,
32)(31, 33)(34, 36)(35, 37)(38, 40)(39, 41)(42, 43)(44, 45)(46, 48)(47, 49)(50,
53)(51, 52)(54, 55)(56, 57)(58, 59)(60, 61)(62, 63)(64, 65)(66, 67)(68, 69)(70,
73)(71, 72)(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, 105)(103, 104)(106, 108)(107,
109)(118, 119)(120, 121)(122, 124)(123, 125)(126, 127)(128, 129)(130, 133)(131,
132)(136, 139)(137, 138)(145, 148)(146, 147)(149, 152)(150, 151)(153, 155)(154,
156)(157, 158)(159, 160)(161, 164)(162, 163)(165, 166)(167, 168)(169, 170)(171,
172)(173, 174)(175, 176)(177, 178)(179, 180)(181, 182)(183, 184)(185, 186)(187,
188)(189, 191)(190, 192)
f: (1, 16, 21, 135, 15, 112, 143, 113, 14, 134, 20, 17)(2, 75, 53, 9, 83, 174,
158, 58, 39, 148, 73, 42)(3, 44, 72, 146, 40, 61, 159, 175, 84, 6, 51, 77)(4,
45, 71, 147, 38, 60, 160, 176, 85, 8, 52, 76)(5, 74, 50, 7, 82, 173, 157, 59,
41, 145, 70, 43)(10, 178, 54, 161, 171, 67, 150, 165, 81, 156, 46, 64)(11, 62,
49, 153, 79, 167, 149, 68, 169, 162, 56, 180)(12, 177, 55, 164, 172, 66, 151,
166, 80, 154, 48, 65)(13, 63, 47, 155, 78, 168, 152, 69, 170, 163, 57, 179)(18,
144, 19, 114, 141, 116, 111, 142, 110, 117, 140, 115)(22, 133, 132, 25, 185,
102, 35, 128, 126, 34, 104, 187)(23, 186, 105, 37, 129, 127, 36, 103, 188, 24,
130, 131)(26, 106, 125, 32, 118, 181, 27, 108, 123, 30, 119, 182)(28, 183, 120,
33, 124, 109, 29, 184, 121, 31, 122, 107)(86, 189, 99, 101, 190, 89, 92, 138,
97, 94, 136, 91)(87, 191, 98, 100, 192, 88, 93, 137, 96, 95, 139, 90)
g: (1, 14)(2, 84)(3, 39)(4, 41)(5, 85)(6, 42)(7, 60)(8, 43)(9, 61)(10, 170)(11,
80)(12, 169)(13, 81)(16, 113)(17, 134)(18, 140)(19, 110)(21, 143)(22, 187)(23,
127)(24, 188)(25, 126)(26, 120)(27, 121)(28, 125)(29, 123)(30, 109)(31, 181)(32,
107)(33, 182)(34, 132)(35, 102)(36, 131)(37, 105)(38, 82)(40, 83)(44, 58)(45,
59)(46, 57)(47, 150)(48, 56)(49, 151)(50, 160)(51, 73)(52, 70)(53, 159)(54,
152)(55, 149)(62, 166)(63, 165)(64, 163)(65, 162)(66, 153)(67, 155)(68, 177)(69,
178)(71, 157)(72, 158)(74, 176)(75, 175)(76, 145)(77, 148)(78, 171)(79, 172)(86,
191)(87, 189)(88, 97)(89, 96)(90, 99)(91, 98)(92, 137)(93, 138)(94, 192)(95,
190)(100, 136)(101, 139)(103, 130)(104, 133)(106, 183)(108, 184)(111, 141)(112,
135)(114, 142)(117, 144)(118, 122)(119, 124)(128, 185)(129, 186)(146, 174)(147,
173)(154, 180)(156, 179)(161, 168)(164, 167)
C4[ 192, 181 ]
192
-1 2 3 4 5
-2 1 188 181 192
-3 1 189 183 186
-4 1 191 184 185
-5 187 1 190 182
-6 122 134 136 130
-7 132 135 125 138
-8 133 134 124 139
-9 123 135 137 131
-10 136 129 119 141
-11 126 138 140 120
-12 128 139 118 141
-13 121 137 127 140
-14 39 84 41 85
-15 38 82 83 40
-16 44 45 74 75
-17 77 42 43 76
-18 47 80 81 49
-19 78 46 79 48
-20 70 51 73 52
-21 71 50 72 53
-22 66 79 74 85
-23 77 69 81 83
-24 67 78 84 75
-25 68 80 82 76
-26 58 80 74 54
-27 55 59 81 75
-28 77 56 78 60
-29 57 79 61 76
-30 66 70 83 64
-31 68 71 84 63
-32 67 82 73 65
-33 69 72 62 85
-34 55 70 60 62
-35 56 59 71 65
-36 61 73 63 54
-37 57 58 72 64
-38 88 15 126 107
-39 14 106 129 87
-40 89 15 127 109
-41 14 128 86 108
-42 100 103 17 118
-43 101 104 17 119
-44 99 16 105 120
-45 121 102 16 98
-46 123 105 19 97
-47 122 103 18 95
-48 102 125 19 96
-49 124 104 94 18
-50 133 92 106 21
-51 91 107 20 131
-52 132 90 20 109
-53 93 108 130 21
-54 111 36 26 86
-55 34 111 27 87
-56 110 89 35 28
-57 88 110 37 29
-58 90 113 26 37
-59 35 91 113 27
-60 34 112 93 28
-61 112 36 92 29
-62 33 34 115 97
-63 36 115 96 31
-64 37 114 94 30
-65 35 114 95 32
-66 22 100 117 30
-67 24 101 117 32
-68 99 25 116 31
-69 33 23 116 98
-70 99 34 30 20
-71 100 35 31 21
-72 33 101 37 21
-73 36 20 32 98
-74 22 89 26 16
-75 88 24 16 27
-76 25 17 29 87
-77 23 17 28 86
-78 24 90 28 19
-79 22 91 29 19
-80 25 26 93 18
-81 23 92 27 18
-82 25 15 97 32
-83 23 15 30 96
-84 24 14 94 31
-85 22 33 14 95
-86 77 167 41 54
-87 55 168 39 76
-88 166 57 38 75
-89 165 56 40 74
-90 78 177 58 52
-91 79 178 59 51
-92 81 180 50 61
-93 80 179 60 53
-94 49 84 173 64
-95 47 85 174 65
-96 176 48 83 63
-97 46 82 62 175
-98 45 69 73 172
-99 44 68 70 171
-100 66 71 170 42
-101 67 169 72 43
-102 45 157 48 162
-103 47 159 161 42
-104 49 160 43 164
-105 44 46 158 163
-106 154 39 50 161
-107 155 38 51 162
-108 156 41 53 164
-109 40 52 163 153
-110 56 57 171 172
-111 55 169 170 54
-112 60 61 173 174
-113 176 58 59 175
-114 167 168 64 65
-115 165 166 62 63
-116 177 68 178 69
-117 66 67 179 180
-118 12 150 173 42
-119 151 174 10 43
-120 11 44 176 152
-121 45 13 149 175
-122 47 147 169 6
-123 46 145 172 9
-124 146 49 170 8
-125 48 148 171 7
-126 11 177 145 38
-127 13 178 148 40
-128 12 147 180 41
-129 146 179 39 10
-130 168 6 150 53
-131 165 51 9 152
-132 166 149 7 52
-133 167 50 8 151
-134 145 148 6 8
-135 146 147 7 9
-136 157 6 10 153
-137 154 13 160 9
-138 11 156 159 7
-139 12 155 158 8
-140 11 13 150 151
-141 12 149 152 10
-142 161 162 163 164
-143 157 158 159 160
-144 154 155 156 153
-145 123 134 189 126
-146 124 135 190 129
-147 122 135 192 128
-148 134 125 191 127
-149 121 132 189 141
-150 190 118 140 130
-151 133 192 140 119
-152 191 141 120 131
-153 187 144 136 109
-154 144 137 106 185
-155 144 188 139 107
-156 144 138 108 186
-157 143 102 136 181
-158 143 105 182 139
-159 143 103 138 184
-160 143 104 137 183
-161 189 103 106 142
-162 102 190 107 142
-163 192 105 109 142
-164 191 104 108 142
-165 89 115 181 131
-166 88 132 115 182
-167 133 114 184 86
-168 114 183 130 87
-169 111 122 101 185
-170 100 111 124 186
-171 99 110 188 125
-172 110 187 123 98
-173 112 94 118 185
-174 112 95 119 186
-175 121 188 113 97
-176 187 113 96 120
-177 90 126 181 116
-178 91 116 127 182
-179 93 117 129 184
-180 92 117 128 183
-181 165 177 2 157
-182 166 178 158 5
-183 3 168 180 160
-184 167 179 4 159
-185 154 4 169 173
-186 156 3 170 174
-187 176 5 172 153
-188 155 2 171 175
-189 145 3 149 161
-190 146 5 150 162
-191 4 148 152 164
-192 2 147 151 163
0