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