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