Graph forms
for C4 [ 192, 196 ] = SS[192,84]
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On this page are computer-accessible forms for the graph C4[ 192, 196 ] =
SS[192,84].
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {58, 59}, {162, 163}, {1, 3}, {161, 163}, {57, 59}, {1, 2}, {1,
5}, {179, 183}, {162, 166}, {161, 165}, {160, 164}, {58, 62}, {56, 60}, {120,
124}, {121, 125}, {122, 126}, {123, 127}, {1, 4}, {123, 126}, {58, 60}, {162,
164}, {160, 166}, {123, 125}, {58, 61}, {162, 165}, {123, 124}, {116, 124},
{180, 188}, {179, 187}, {117, 125}, {118, 126}, {119, 127}, {55, 62}, {54, 61},
{182, 189}, {181, 190}, {51, 63}, {180, 184}, {176, 188}, {115, 127}, {50, 63},
{177, 190}, {182, 185}, {181, 186}, {178, 189}, {10, 26}, {168, 184}, {167,
183}, {12, 28}, {107, 120}, {170, 185}, {169, 186}, {172, 184}, {175, 187},
{174, 186}, {173, 185}, {11, 29}, {13, 27}, {108, 122}, {110, 121}, {10, 18},
{164, 188}, {163, 187}, {11, 19}, {12, 21}, {13, 20}, {109, 119}, {165, 190},
{166, 189}, {171, 183}, {15, 47}, {17, 49}, {140, 175}, {144, 179}, {80, 116},
{146, 182}, {12, 41}, {13, 40}, {145, 180}, {147, 181}, {81, 118}, {82, 117},
{136, 175}, {6, 46}, {15, 39}, {14, 38}, {13, 37}, {10, 34}, {7, 47}, {80, 120},
{134, 174}, {133, 172}, {135, 173}, {15, 36}, {81, 122}, {82, 121}, {10, 38},
{158, 178}, {14, 34}, {11, 39}, {157, 176}, {159, 177}, {11, 36}, {12, 35},
{132, 171}, {6, 54}, {154, 170}, {69, 117}, {68, 116}, {67, 115}, {70, 118}, {8,
57}, {153, 168}, {150, 167}, {155, 169}, {6, 53}, {156, 175}, {152, 171}, {148,
167}, {16, 35}, {7, 52}, {128, 179}, {17, 37}, {130, 182}, {6, 51}, {155, 174},
{153, 172}, {7, 50}, {129, 180}, {131, 181}, {154, 173}, {79, 119}, {158, 166},
{138, 178}, {8, 49}, {157, 164}, {17, 40}, {16, 41}, {9, 48}, {137, 176}, {8,
50}, {159, 165}, {139, 177}, {145, 171}, {8, 51}, {9, 53}, {149, 169}, {79,
115}, {142, 178}, {144, 172}, {146, 174}, {9, 52}, {141, 176}, {9, 55}, {151,
169}, {150, 168}, {148, 170}, {16, 46}, {14, 48}, {143, 177}, {147, 173}, {7,
56}, {156, 163}, {152, 167}, {151, 168}, {149, 170}, {27, 90}, {33, 96}, {26,
88}, {26, 89}, {59, 120}, {25, 93}, {29, 89}, {29, 88}, {24, 94}, {60, 122},
{28, 90}, {25, 95}, {62, 121}, {61, 119}, {23, 92}, {43, 96}, {28, 87}, {27,
87}, {45, 97}, {22, 91}, {33, 111}, {44, 98}, {32, 111}, {33, 113}, {32, 113},
{57, 107}, {30, 74}, {56, 108}, {31, 73}, {55, 110}, {54, 109}, {43, 75}, {44,
76}, {42, 75}, {45, 76}, {44, 78}, {16, 115}, {45, 78}, {43, 72}, {35, 71}, {57,
93}, {56, 92}, {45, 73}, {17, 116}, {40, 77}, {43, 77}, {44, 74}, {32, 71}, {42,
77}, {41, 78}, {34, 74}, {33, 72}, {55, 94}, {47, 70}, {38, 79}, {39, 76}, {30,
114}, {49, 93}, {37, 73}, {36, 72}, {31, 114}, {54, 91}, {46, 67}, {42, 71},
{38, 75}, {30, 112}, {48, 94}, {31, 112}, {19, 99}, {37, 85}, {35, 83}, {21,
101}, {20, 102}, {51, 65}, {50, 64}, {36, 86}, {25, 106}, {47, 92}, {19, 103},
{53, 65}, {52, 64}, {18, 103}, {49, 68}, {48, 69}, {46, 91}, {42, 95}, {25,
108}, {24, 109}, {23, 98}, {18, 100}, {52, 66}, {34, 84}, {22, 97}, {53, 66},
{39, 80}, {22, 110}, {24, 96}, {15, 118}, {40, 81}, {28, 101}, {18, 104}, {14,
117}, {41, 82}, {19, 104}, {21, 105}, {30, 98}, {23, 107}, {20, 105}, {27, 102},
{20, 106}, {31, 97}, {29, 99}, {26, 100}, {21, 106}, {32, 95}, {24, 103}, {23,
104}, {22, 105}, {59, 161}, {60, 160}, {61, 161}, {62, 160}, {63, 156}, {63,
152}, {2, 183}, {5, 189}, {2, 187}, {4, 190}, {5, 191}, {3, 184}, {5, 185},
{124, 192}, {2, 191}, {125, 192}, {4, 186}, {3, 188}, {127, 191}, {126, 191},
{74, 136}, {3, 192}, {72, 139}, {73, 138}, {76, 143}, {77, 142}, {78, 141}, {79,
140}, {4, 192}, {75, 140}, {86, 158}, {84, 157}, {85, 159}, {83, 152}, {86,
154}, {84, 153}, {71, 137}, {85, 155}, {83, 156}, {69, 149}, {70, 150}, {88,
137}, {90, 139}, {68, 150}, {69, 151}, {70, 148}, {68, 151}, {89, 138}, {88,
141}, {90, 143}, {67, 149}, {67, 148}, {89, 142}, {66, 154}, {64, 153}, {95,
134}, {65, 155}, {83, 137}, {87, 140}, {92, 135}, {93, 134}, {94, 133}, {66,
158}, {84, 136}, {64, 157}, {86, 139}, {65, 159}, {80, 143}, {81, 142}, {82,
141}, {85, 138}, {87, 136}, {91, 132}, {112, 144}, {113, 145}, {114, 146}, {100,
134}, {101, 135}, {102, 133}, {96, 133}, {97, 132}, {98, 135}, {99, 132}, {103,
128}, {105, 129}, {106, 130}, {107, 131}, {104, 131}, {111, 131}, {109, 128},
{108, 130}, {110, 129}, {112, 128}, {113, 129}, {114, 130}, {99, 145}, {100,
146}, {101, 147}, {102, 144}, {111, 147} }>;
(II) A more general form is to represent the graph as the orbit of {58, 59}
under the group generated by the following permutations:
a: (2, 4)(3, 5)(6, 8)(7, 9)(10, 11)(12, 13)(14, 15)(16, 17)(18, 19)(20, 21)(22,
25)(23, 24)(26, 29)(27, 28)(30, 33)(31, 32)(34, 36)(35, 37)(38, 39)(40, 41)(42,
45)(43, 44)(46, 49)(47, 48)(50, 53)(54, 57)(55, 56)(59, 61)(60, 62)(63, 65)(64,
66)(67, 68)(69, 70)(71, 73)(72, 74)(75, 76)(77, 78)(79, 80)(81, 82)(83, 85)(84,
86)(87, 90)(88, 89)(91, 93)(92, 94)(95, 97)(96, 98)(99, 100)(101, 102)(103,
104)(105, 106)(107, 109)(108, 110)(111, 112)(113, 114)(115, 116)(117, 118)(119,
120)(121, 122)(124, 127)(125, 126)(128, 131)(129, 130)(132, 134)(133, 135)(136,
139)(137, 138)(140, 143)(141, 142)(144, 147)(145, 146)(148, 151)(149, 150)(152,
155)(153, 154)(156, 159)(157, 158)(163, 165)(164, 166)(167, 169)(168, 170)(171,
174)(172, 173)(175, 177)(176, 178)(179, 181)(180, 182)(183, 186)(184, 185)(187,
190)(188, 189)(191, 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, 22, 50, 38)(2, 110, 63, 14)(3, 91, 64, 79)(4, 97, 7, 75)(5, 105, 8,
10)(6, 84, 127, 180)(9, 175, 125, 171)(11, 86, 90, 80)(12, 68, 103, 166)(13,
107, 89, 173)(15, 72, 177, 76)(16, 168, 109, 164)(17, 104, 178, 101)(18, 189,
21, 49)(19, 158, 28, 116)(20, 57, 26, 185)(23, 142, 147, 37)(24, 162, 41,
150)(25, 134, 146, 130)(27, 120, 29, 154)(30, 122, 32, 155)(31, 56, 42, 186)(33,
159, 44, 118)(34, 191, 129, 51)(35, 151, 128, 160)(36, 139, 143, 39)(40, 131,
138, 135)(43, 190, 45, 47)(46, 153, 119, 188)(48, 187, 121, 152)(52, 140, 192,
132)(53, 136, 123, 145)(54, 157, 115, 184)(55, 156, 117, 183)(58, 137, 149,
144)(59, 88, 170, 102)(60, 71, 169, 112)(61, 176, 67, 172)(62, 83, 69, 179)(65,
74, 126, 113)(66, 87, 124, 99)(70, 96, 165, 78)(73, 92, 77, 181)(81, 111, 85,
98)(82, 167, 94, 163)(93, 100, 182, 106)(95, 174, 114, 108)(133, 161, 141,
148)
c: (2, 3)(4, 5)(6, 9)(7, 8)(10, 12)(11, 13)(14, 16)(15, 17)(18, 21)(19, 20)(22,
24)(23, 25)(26, 28)(27, 29)(30, 32)(31, 33)(34, 35)(36, 37)(38, 41)(39, 40)(42,
44)(43, 45)(46, 48)(47, 49)(51, 52)(54, 55)(56, 57)(59, 60)(61, 62)(63, 64)(65,
66)(67, 69)(68, 70)(71, 74)(72, 73)(75, 78)(76, 77)(79, 82)(80, 81)(83, 84)(85,
86)(87, 88)(89, 90)(91, 94)(92, 93)(95, 98)(96, 97)(99, 102)(100, 101)(103,
105)(104, 106)(107, 108)(109, 110)(111, 114)(112, 113)(115, 117)(116, 118)(119,
121)(120, 122)(124, 126)(125, 127)(128, 129)(130, 131)(132, 133)(134, 135)(136,
137)(138, 139)(140, 141)(142, 143)(144, 145)(146, 147)(148, 151)(152, 153)(154,
155)(156, 157)(158, 159)(160, 161)(163, 164)(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, 190)(191, 192)
d: (1, 18, 192, 19, 123, 29, 191, 26)(2, 10, 3, 103, 125, 99, 127, 88)(4, 104,
124, 11, 126, 89, 5, 100)(6, 12, 63, 87, 64, 102, 9, 105)(7, 13, 66, 106, 65,
101, 8, 90)(14, 180, 109, 82, 171, 79, 176, 179)(15, 81, 178, 182, 174, 181,
107, 80)(16, 83, 175, 84, 172, 94, 110, 91)(17, 86, 108, 85, 173, 93, 177,
92)(20, 53, 21, 51, 28, 50, 27, 52)(22, 46, 35, 156, 136, 153, 133, 55)(23, 116,
36, 122, 138, 185, 134, 190)(24, 121, 132, 115, 137, 187, 34, 184)(25, 159, 135,
49, 139, 56, 37, 154)(30, 151, 33, 58, 45, 148, 42, 162)(31, 149, 32, 161, 44,
150, 43, 160)(38, 188, 128, 117, 145, 119, 141, 183)(39, 118, 142, 189, 146,
186, 131, 120)(40, 158, 130, 155, 147, 57, 143, 47)(41, 152, 140, 157, 144, 48,
129, 54)(59, 76, 70, 77, 166, 114, 169, 111)(60, 73, 170, 95, 165, 98, 68,
72)(61, 78, 167, 75, 164, 112, 69, 113)(62, 97, 67, 71, 163, 74, 168, 96)
C4[ 192, 196 ]
192
-1 2 3 4 5
-2 187 1 191 183
-3 1 188 192 184
-4 1 190 192 186
-5 1 189 191 185
-6 46 51 53 54
-7 56 47 50 52
-8 57 49 50 51
-9 55 48 52 53
-10 34 26 38 18
-11 36 39 29 19
-12 35 28 41 21
-13 37 27 40 20
-14 34 48 38 117
-15 36 47 39 118
-16 35 46 115 41
-17 37 49 116 40
-18 100 103 104 10
-19 11 99 103 104
-20 13 102 105 106
-21 12 101 105 106
-22 110 91 105 97
-23 92 104 107 98
-24 103 94 96 109
-25 93 95 106 108
-26 88 89 100 10
-27 13 90 102 87
-28 12 90 101 87
-29 11 88 99 89
-30 112 114 74 98
-31 112 114 73 97
-32 111 113 71 95
-33 111 113 72 96
-34 14 84 74 10
-35 12 16 71 83
-36 11 15 72 86
-37 13 17 73 85
-38 79 14 75 10
-39 11 80 15 76
-40 77 13 81 17
-41 12 78 16 82
-42 77 71 95 75
-43 77 72 96 75
-44 78 74 76 98
-45 78 73 97 76
-46 67 91 16 6
-47 15 70 92 7
-48 14 69 94 9
-49 68 93 17 8
-50 7 8 63 64
-51 6 8 63 65
-52 66 7 9 64
-53 66 6 9 65
-54 91 6 61 109
-55 110 94 62 9
-56 92 60 7 108
-57 59 93 8 107
-58 59 60 61 62
-59 57 58 161 120
-60 56 122 58 160
-61 58 161 119 54
-62 55 121 58 160
-63 156 50 51 152
-64 157 50 52 153
-65 155 159 51 53
-66 154 158 52 53
-67 46 115 148 149
-68 49 116 150 151
-69 48 149 117 151
-70 47 148 150 118
-71 35 137 42 32
-72 33 36 139 43
-73 45 37 138 31
-74 44 34 136 30
-75 38 140 42 43
-76 44 143 45 39
-77 40 42 43 142
-78 44 45 41 141
-79 38 115 140 119
-80 143 39 116 120
-81 122 40 118 142
-82 121 117 41 141
-83 35 156 137 152
-84 34 157 136 153
-85 155 37 159 138
-86 154 36 158 139
-87 136 27 28 140
-88 26 137 29 141
-89 26 138 29 142
-90 143 27 28 139
-91 22 132 46 54
-92 23 56 47 135
-93 57 134 25 49
-94 55 133 24 48
-95 134 25 42 32
-96 33 133 24 43
-97 22 132 45 31
-98 44 23 135 30
-99 132 145 29 19
-100 134 146 26 18
-101 135 147 28 21
-102 133 144 27 20
-103 24 18 128 19
-104 23 18 19 131
-105 22 129 20 21
-106 25 20 130 21
-107 23 57 120 131
-108 56 122 25 130
-109 24 128 119 54
-110 22 55 121 129
-111 33 147 32 131
-112 144 128 30 31
-113 33 145 129 32
-114 146 30 31 130
-115 67 79 16 127
-116 68 80 124 17
-117 14 69 125 82
-118 15 70 81 126
-119 79 61 127 109
-120 80 124 59 107
-121 110 125 82 62
-122 81 60 126 108
-123 124 125 126 127
-124 123 192 116 120
-125 121 123 192 117
-126 122 123 191 118
-127 123 191 115 119
-128 112 179 103 109
-129 110 113 180 105
-130 114 182 106 108
-131 111 104 181 107
-132 99 91 171 97
-133 102 94 172 96
-134 100 93 95 174
-135 101 92 173 98
-136 84 74 87 175
-137 88 176 71 83
-138 89 178 73 85
-139 177 90 72 86
-140 79 75 87 175
-141 88 176 78 82
-142 77 89 178 81
-143 177 90 80 76
-144 112 102 179 172
-145 99 113 180 171
-146 100 114 182 174
-147 111 101 181 173
-148 67 167 70 170
-149 67 69 169 170
-150 68 167 168 70
-151 68 69 168 169
-152 167 83 171 63
-153 168 84 172 64
-154 66 170 173 86
-155 169 85 174 65
-156 83 63 163 175
-157 176 84 64 164
-158 66 166 178 86
-159 165 177 85 65
-160 166 60 62 164
-161 165 59 61 163
-162 165 166 163 164
-163 187 156 161 162
-164 188 157 160 162
-165 190 159 161 162
-166 189 158 160 162
-167 148 150 183 152
-168 150 151 184 153
-169 155 149 151 186
-170 154 148 149 185
-171 132 145 183 152
-172 133 144 184 153
-173 154 135 147 185
-174 155 134 146 186
-175 187 156 136 140
-176 188 157 137 141
-177 143 190 159 139
-178 189 158 138 142
-179 187 144 128 183
-180 188 145 129 184
-181 190 147 131 186
-182 189 146 130 185
-183 2 167 179 171
-184 3 168 180 172
-185 5 170 182 173
-186 4 169 181 174
-187 2 179 163 175
-188 176 3 180 164
-189 166 178 5 182
-190 165 177 4 181
-191 2 5 126 127
-192 3 124 4 125
0