Graph forms
for C4 [ 192, 194 ] = SS[192,82]
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On this page are computer-accessible forms for the graph C4[ 192, 194 ] =
SS[192,82].
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {1, 3}, {84, 86}, {1, 2}, {180, 183}, {1, 5}, {178, 182}, {177,
181}, {32, 36}, {1, 4}, {144, 149}, {33, 36}, {82, 87}, {34, 36}, {144, 150},
{80, 86}, {83, 85}, {35, 36}, {144, 151}, {144, 152}, {81, 88}, {83, 90}, {81,
91}, {176, 187}, {179, 184}, {80, 93}, {84, 89}, {82, 92}, {78, 94}, {141, 157},
{72, 90}, {142, 156}, {141, 159}, {77, 95}, {141, 158}, {175, 188}, {171, 184},
{168, 187}, {76, 88}, {174, 186}, {173, 185}, {143, 155}, {137, 157}, {77, 88},
{143, 154}, {139, 158}, {138, 159}, {128, 149}, {130, 151}, {129, 150}, {142,
153}, {79, 87}, {138, 146}, {137, 145}, {69, 92}, {133, 156}, {131, 153}, {142,
148}, {78, 85}, {172, 183}, {167, 188}, {164, 191}, {160, 187}, {71, 91}, {170,
182}, {169, 181}, {166, 186}, {165, 185}, {162, 190}, {161, 189}, {143, 147},
{142, 146}, {73, 85}, {74, 87}, {75, 86}, {134, 155}, {132, 154}, {143, 145},
{70, 89}, {140, 147}, {139, 148}, {14, 46}, {27, 59}, {15, 47}, {12, 45}, {29,
60}, {27, 58}, {25, 56}, {14, 44}, {158, 188}, {11, 40}, {156, 191}, {148, 183},
{26, 57}, {23, 52}, {75, 104}, {13, 41}, {157, 185}, {154, 190}, {153, 189},
{135, 163}, {27, 63}, {26, 62}, {22, 50}, {15, 43}, {64, 100}, {67, 103}, {74,
110}, {22, 51}, {159, 186}, {31, 58}, {30, 59}, {28, 57}, {135, 162}, {12, 42},
{30, 56}, {26, 60}, {23, 49}, {73, 111}, {75, 109}, {128, 166}, {26, 61}, {152,
191}, {146, 181}, {145, 182}, {65, 102}, {66, 101}, {130, 165}, {31, 55}, {150,
190}, {149, 189}, {134, 174}, {28, 53}, {136, 161}, {129, 168}, {76, 102}, {29,
54}, {147, 184}, {31, 52}, {132, 175}, {10, 38}, {140, 160}, {136, 164}, {19,
63}, {68, 104}, {73, 101}, {10, 39}, {141, 160}, {24, 53}, {19, 62}, {74, 103},
{11, 37}, {29, 51}, {28, 50}, {25, 55}, {24, 54}, {131, 173}, {18, 61}, {30,
49}, {79, 96}, {15, 63}, {12, 61}, {13, 62}, {133, 176}, {76, 112}, {13, 48},
{16, 80}, {50, 114}, {49, 113}, {18, 83}, {42, 107}, {37, 100}, {19, 82}, {10,
72}, {54, 116}, {51, 113}, {43, 105}, {40, 106}, {18, 81}, {38, 98}, {55, 115},
{41, 108}, {42, 111}, {22, 80}, {53, 115}, {52, 114}, {44, 106}, {43, 109}, {39,
97}, {19, 84}, {41, 110}, {12, 68}, {24, 81}, {37, 108}, {60, 117}, {25, 83},
{25, 82}, {40, 99}, {10, 70}, {44, 96}, {39, 107}, {24, 84}, {13, 65}, {11, 71},
{56, 116}, {58, 118}, {14, 67}, {15, 66}, {11, 69}, {48, 126}, {14, 64}, {59,
117}, {38, 105}, {48, 127}, {57, 118}, {20, 68}, {53, 101}, {16, 65}, {54, 103},
{45, 124}, {40, 121}, {38, 119}, {20, 69}, {16, 66}, {51, 97}, {47, 125}, {21,
71}, {18, 64}, {17, 67}, {21, 70}, {49, 98}, {28, 72}, {17, 68}, {46, 123}, {20,
65}, {21, 67}, {50, 100}, {33, 119}, {21, 66}, {151, 192}, {52, 99}, {23, 79},
{29, 69}, {23, 78}, {35, 122}, {32, 121}, {31, 70}, {30, 71}, {57, 96}, {34,
120}, {22, 77}, {155, 192}, {27, 64}, {17, 77}, {44, 112}, {20, 72}, {62, 99},
{56, 102}, {63, 97}, {16, 79}, {55, 104}, {39, 120}, {37, 122}, {17, 78}, {61,
98}, {60, 94}, {163, 192}, {58, 95}, {59, 93}, {48, 91}, {46, 92}, {8, 124},
{45, 89}, {43, 94}, {47, 90}, {41, 95}, {9, 126}, {42, 93}, {6, 127}, {7, 125},
{6, 123}, {7, 135}, {8, 136}, {6, 135}, {9, 136}, {8, 139}, {9, 138}, {7, 128},
{9, 129}, {8, 130}, {7, 140}, {6, 137}, {33, 131}, {34, 134}, {32, 133}, {35,
132}, {32, 137}, {35, 138}, {34, 139}, {33, 140}, {47, 130}, {45, 128}, {46,
129}, {4, 183}, {5, 182}, {2, 181}, {5, 191}, {2, 185}, {3, 184}, {2, 190}, {3,
189}, {3, 188}, {5, 186}, {4, 187}, {103, 167}, {114, 176}, {101, 166}, {4,
192}, {76, 132}, {123, 179}, {107, 162}, {73, 131}, {106, 160}, {126, 180}, {96,
171}, {106, 161}, {111, 164}, {75, 134}, {104, 165}, {105, 164}, {124, 177},
{102, 168}, {74, 133}, {108, 163}, {109, 162}, {110, 161}, {125, 178}, {97,
177}, {98, 178}, {99, 179}, {100, 180}, {117, 165}, {118, 167}, {122, 171},
{120, 170}, {112, 163}, {117, 166}, {121, 172}, {116, 172}, {127, 167}, {115,
170}, {115, 169}, {113, 173}, {114, 175}, {118, 168}, {119, 169}, {113, 174},
{116, 171}, {119, 151}, {122, 152}, {87, 180}, {85, 177}, {86, 178}, {127, 152},
{88, 179}, {91, 176}, {112, 156}, {120, 149}, {124, 145}, {126, 147}, {121,
150}, {123, 148}, {125, 146}, {108, 158}, {92, 175}, {95, 172}, {89, 173}, {90,
174}, {93, 169}, {94, 170}, {105, 157}, {107, 159}, {109, 153}, {110, 154},
{111, 155} }>;
(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, 4)(3, 5)(6, 7)(8, 9)(10, 11)(12, 13)(14, 15)(16, 17)(18, 19)(28, 29)(30,
31)(32, 33)(34, 35)(37, 39)(38, 40)(41, 42)(43, 44)(45, 48)(46, 47)(49, 52)(50,
51)(53, 54)(55, 56)(57, 60)(58, 59)(61, 62)(63, 64)(65, 68)(66, 67)(69, 72)(70,
71)(73, 74)(75, 76)(77, 80)(78, 79)(81, 84)(82, 83)(85, 87)(86, 88)(89, 91)(90,
92)(93, 95)(94, 96)(97, 100)(98, 99)(101, 103)(102, 104)(105, 106)(107,
108)(109, 112)(110, 111)(113, 114)(115, 116)(117, 118)(119, 121)(120, 122)(123,
125)(124, 126)(127, 128)(129, 130)(131, 133)(132, 134)(137, 140)(138, 139)(145,
147)(146, 148)(149, 152)(150, 151)(153, 156)(154, 155)(157, 160)(158, 159)(161,
164)(162, 163)(165, 168)(166, 167)(169, 172)(170, 171)(173, 176)(174, 175)(177,
180)(178, 179)(181, 183)(182, 184)(185, 187)(186, 188)(189, 191)(190, 192) (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, 20, 142, 26, 36, 27, 143, 21)(2, 65, 153, 57, 34, 64, 145, 71)(3, 72,
148, 61, 32, 59, 154, 66)(4, 68, 156, 60, 35, 63, 147, 70)(5, 69, 146, 62, 33,
58, 155, 67)(6, 49, 150, 80, 161, 53, 158, 83)(7, 52, 151, 77, 164, 54, 159,
82)(8, 81, 157, 56, 162, 79, 149, 50)(9, 84, 160, 55, 163, 78, 152, 51)(10, 183,
12, 133, 117, 132, 15, 184)(11, 181, 13, 131, 118, 134, 14, 182)(16, 189, 28,
139, 18, 137, 30, 190)(17, 191, 29, 138, 19, 140, 31, 192)(22, 136, 24, 141, 25,
135, 23, 144)(37, 177, 48, 173, 168, 75, 44, 170)(38, 172, 42, 74, 166, 175, 47,
179)(39, 180, 45, 176, 165, 76, 43, 171)(40, 169, 41, 73, 167, 174, 46, 178)(85,
127, 113, 129, 86, 106, 115, 108)(87, 128, 114, 130, 88, 105, 116, 107)(89, 187,
104, 112, 94, 122, 97, 126)(90, 123, 98, 121, 93, 110, 101, 188)(91, 185, 102,
109, 96, 120, 100, 124)(92, 125, 99, 119, 95, 111, 103, 186)
c: (1, 10, 116, 141, 115, 11)(2, 72, 172, 159, 55, 37)(3, 38, 54, 160, 170,
71)(4, 39, 56, 158, 169, 69)(5, 70, 171, 157, 53, 40)(6, 73, 62, 156, 45, 79)(7,
78, 48, 153, 61, 74)(8, 80, 46, 155, 63, 76)(9, 75, 64, 154, 47, 77)(12, 87,
135, 85, 13, 142)(14, 143, 15, 88, 136, 86)(16, 123, 111, 19, 112, 124)(17, 126,
109, 18, 110, 125)(20, 183, 107, 25, 108, 181)(21, 184, 105, 24, 106, 182)(22,
129, 134, 27, 132, 130)(23, 127, 131, 26, 133, 128)(28, 121, 186, 31, 122,
185)(29, 187, 120, 30, 188, 119)(32, 166, 52, 152, 173, 57)(33, 60, 176, 149,
49, 167)(34, 59, 175, 151, 51, 168)(35, 165, 50, 150, 174, 58)(36, 117, 114,
144, 113, 118)(41, 146, 68, 180, 162, 83)(42, 82, 163, 177, 65, 148)(43, 81,
161, 178, 67, 147)(44, 145, 66, 179, 164, 84)(89, 96, 137, 101, 99, 191)(90, 95,
138, 104, 100, 190)(91, 189, 98, 103, 140, 94)(92, 192, 97, 102, 139, 93)
d: (1, 12, 36, 15)(2, 45, 34, 43)(3, 68, 32, 63)(4, 61, 35, 66)(5, 42, 33,
47)(6, 51, 161, 55)(7, 174, 164, 169)(8, 170, 162, 173)(9, 53, 163, 49)(10, 142,
117, 143)(11, 87, 118, 88)(13, 114, 14, 116)(16, 187, 18, 122)(17, 121, 19,
188)(20, 133, 27, 184)(21, 183, 26, 132)(22, 106, 25, 127)(23, 129, 24, 108)(28,
112, 30, 126)(29, 110, 31, 123)(37, 79, 168, 81)(38, 146, 166, 155)(39, 153,
165, 145)(40, 82, 167, 77)(41, 52, 46, 54)(44, 56, 48, 50)(57, 76, 71, 180)(58,
179, 69, 74)(59, 147, 72, 156)(60, 154, 70, 148)(62, 175, 67, 172)(64, 171, 65,
176)(73, 151, 178, 159)(75, 157, 177, 149)(78, 150, 84, 158)(80, 160, 83,
152)(85, 144, 86, 141)(89, 139, 94, 190)(90, 191, 93, 140)(91, 100, 96, 102)(92,
103, 95, 99)(97, 189, 104, 137)(98, 138, 101, 192)(105, 181, 128, 134)(107, 131,
130, 182)(109, 185, 124, 120)(111, 119, 125, 186)(113, 136, 115, 135)
e: (2, 3)(4, 5)(6, 8)(7, 9)(10, 11)(12, 14)(13, 15)(20, 21)(22, 23)(24, 25)(26,
27)(28, 30)(29, 31)(32, 34)(33, 35)(37, 38)(39, 40)(41, 43)(42, 44)(45, 46)(47,
48)(49, 50)(51, 52)(53, 56)(54, 55)(57, 59)(58, 60)(61, 64)(62, 63)(65, 66)(67,
68)(69, 70)(71, 72)(73, 76)(74, 75)(77, 78)(79, 80)(81, 83)(82, 84)(85, 88)(86,
87)(89, 92)(90, 91)(93, 96)(94, 95)(97, 99)(98, 100)(101, 102)(103, 104)(105,
108)(106, 107)(109, 110)(111, 112)(113, 114)(115, 116)(117, 118)(119, 122)(120,
121)(123, 124)(125, 126)(127, 130)(128, 129)(131, 132)(133, 134)(135, 136)(137,
139)(138, 140)(142, 143)(145, 148)(146, 147)(149, 150)(151, 152)(153, 154)(155,
156)(157, 158)(159, 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)
f: (1, 16, 141, 19)(2, 80, 159, 63)(3, 79, 160, 62)(4, 65, 158, 82)(5, 66, 157,
84)(6, 54, 156, 71)(7, 60, 153, 49)(8, 55, 155, 72)(9, 58, 154, 50)(10, 124,
115, 111)(11, 123, 116, 112)(12, 120, 85, 119)(13, 188, 87, 187)(14, 121, 88,
122)(15, 185, 86, 186)(17, 36, 18, 144)(20, 139, 25, 192)(21, 137, 24, 191)(22,
138, 27, 190)(23, 140, 26, 189)(28, 136, 31, 143)(29, 142, 30, 135)(32, 81, 152,
67)(33, 61, 149, 78)(34, 83, 151, 68)(35, 64, 150, 77)(37, 46, 172, 76)(38, 45,
170, 73)(39, 177, 169, 42)(40, 179, 171, 44)(41, 175, 180, 168)(43, 173, 178,
166)(47, 165, 75, 174)(48, 167, 74, 176)(51, 146, 59, 162)(52, 147, 57, 161)(53,
164, 70, 145)(56, 163, 69, 148)(89, 182, 101, 105)(90, 130, 104, 134)(91, 127,
103, 133)(92, 183, 102, 108)(93, 107, 97, 181)(94, 131, 98, 128)(95, 132, 100,
129)(96, 106, 99, 184)(109, 113, 125, 117)(110, 114, 126, 118)
C4[ 192, 194 ]
192
-1 2 3 4 5
-2 1 190 181 185
-3 1 188 189 184
-4 187 1 192 183
-5 1 191 182 186
-6 123 135 137 127
-7 135 125 128 140
-8 124 136 139 130
-9 136 126 138 129
-10 70 38 39 72
-11 69 37 71 40
-12 45 68 61 42
-13 48 62 41 65
-14 44 67 46 64
-15 66 47 63 43
-16 66 79 80 65
-17 77 67 78 68
-18 81 61 83 64
-19 82 62 84 63
-20 68 69 72 65
-21 66 67 70 71
-22 77 80 50 51
-23 78 79 49 52
-24 81 84 53 54
-25 55 56 82 83
-26 57 60 61 62
-27 58 59 63 64
-28 57 50 72 53
-29 69 60 51 54
-30 56 59 49 71
-31 55 58 70 52
-32 121 133 36 137
-33 36 140 119 131
-34 134 36 139 120
-35 132 122 36 138
-36 33 34 35 32
-37 11 100 122 108
-38 105 119 10 98
-39 107 97 10 120
-40 11 99 121 106
-41 110 13 95 108
-42 12 111 93 107
-43 15 94 105 109
-44 112 14 106 96
-45 12 89 124 128
-46 123 14 92 129
-47 90 15 125 130
-48 13 91 126 127
-49 23 113 30 98
-50 22 100 114 28
-51 22 113 29 97
-52 99 23 114 31
-53 24 101 115 28
-54 24 103 116 29
-55 25 104 115 31
-56 25 102 116 30
-57 26 28 96 118
-58 27 95 118 31
-59 27 93 117 30
-60 26 94 29 117
-61 12 26 18 98
-62 99 13 26 19
-63 15 27 19 97
-64 100 14 27 18
-65 13 102 16 20
-66 101 15 16 21
-67 14 103 17 21
-68 12 104 17 20
-69 11 92 29 20
-70 89 31 10 21
-71 11 91 30 21
-72 90 28 20 10
-73 111 101 85 131
-74 110 133 103 87
-75 134 104 86 109
-76 88 132 112 102
-77 22 88 17 95
-78 23 17 94 85
-79 23 16 96 87
-80 22 16 93 86
-81 88 24 91 18
-82 25 92 19 87
-83 90 25 18 85
-84 89 24 19 86
-85 78 177 83 73
-86 178 80 84 75
-87 79 180 82 74
-88 77 179 81 76
-89 45 70 84 173
-90 47 72 83 174
-91 176 48 81 71
-92 46 69 82 175
-93 80 59 169 42
-94 78 60 170 43
-95 77 58 172 41
-96 44 57 79 171
-97 177 39 51 63
-98 178 38 49 61
-99 179 40 62 52
-100 37 180 50 64
-101 66 166 73 53
-102 56 168 65 76
-103 67 167 74 54
-104 55 165 68 75
-105 157 38 43 164
-106 44 160 40 161
-107 159 39 162 42
-108 37 158 41 163
-109 162 75 43 153
-110 154 161 41 74
-111 155 73 42 164
-112 44 156 163 76
-113 49 51 173 174
-114 176 50 52 175
-115 55 169 170 53
-116 56 171 172 54
-117 165 166 59 60
-118 57 167 58 168
-119 33 169 38 151
-120 34 170 39 149
-121 40 150 172 32
-122 35 37 171 152
-123 46 179 148 6
-124 45 177 145 8
-125 178 47 146 7
-126 48 147 180 9
-127 167 48 6 152
-128 45 166 149 7
-129 46 168 150 9
-130 165 47 8 151
-131 33 73 173 153
-132 154 35 76 175
-133 176 156 74 32
-134 34 155 75 174
-135 6 7 162 163
-136 161 8 9 164
-137 145 157 6 32
-138 35 146 159 9
-139 34 158 148 8
-140 33 147 160 7
-141 157 158 159 160
-142 156 146 148 153
-143 154 155 145 147
-144 149 150 151 152
-145 143 124 137 182
-146 125 181 138 142
-147 143 126 140 184
-148 123 139 183 142
-149 144 189 128 120
-150 121 144 190 129
-151 144 192 119 130
-152 122 144 191 127
-153 189 109 131 142
-154 110 132 143 190
-155 143 111 134 192
-156 133 112 191 142
-157 137 105 141 185
-158 188 139 108 141
-159 138 107 141 186
-160 187 106 140 141
-161 110 189 136 106
-162 135 190 107 109
-163 112 135 192 108
-164 111 136 191 105
-165 104 117 130 185
-166 101 117 128 186
-167 188 103 127 118
-168 187 102 118 129
-169 93 115 181 119
-170 115 94 182 120
-171 122 116 96 184
-172 121 116 95 183
-173 89 113 185 131
-174 90 134 113 186
-175 132 188 92 114
-176 187 133 91 114
-177 124 181 85 97
-178 125 182 86 98
-179 88 99 123 184
-180 100 126 183 87
-181 177 2 146 169
-182 145 178 5 170
-183 4 180 148 172
-184 3 179 147 171
-185 165 2 157 173
-186 166 5 159 174
-187 176 168 4 160
-188 167 3 158 175
-189 3 149 161 153
-190 154 2 150 162
-191 156 5 152 164
-192 155 4 151 163
0