Graph forms
for C4 [ 192, 193 ] = SS[192,80]
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On this page are computer-accessible forms for the graph C4[ 192, 193 ] =
SS[192,80].
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {1, 3}, {180, 182}, {1, 2}, {1, 5}, {179, 183}, {177, 181}, {81,
85}, {82, 86}, {1, 4}, {144, 149}, {144, 150}, {80, 87}, {144, 151}, {83, 84},
{83, 91}, {144, 152}, {80, 89}, {82, 88}, {178, 184}, {81, 90}, {176, 191}, {34,
50}, {174, 190}, {173, 189}, {140, 156}, {136, 152}, {131, 147}, {129, 145},
{32, 49}, {143, 158}, {142, 159}, {135, 150}, {133, 148}, {76, 93}, {78, 95},
{33, 51}, {128, 146}, {35, 48}, {171, 184}, {142, 157}, {134, 149}, {77, 94},
{79, 92}, {33, 53}, {35, 54}, {140, 153}, {132, 145}, {34, 52}, {141, 155},
{130, 148}, {32, 55}, {168, 191}, {160, 183}, {141, 154}, {137, 158}, {136,
159}, {133, 146}, {132, 147}, {32, 56}, {166, 190}, {165, 189}, {162, 186},
{161, 185}, {35, 59}, {76, 86}, {77, 87}, {78, 84}, {79, 85}, {33, 58}, {172,
183}, {134, 157}, {34, 57}, {32, 60}, {170, 182}, {169, 181}, {33, 61}, {74,
86}, {34, 63}, {35, 62}, {73, 84}, {75, 85}, {137, 151}, {72, 87}, {164, 187},
{163, 188}, {153, 185}, {154, 186}, {26, 59}, {27, 58}, {26, 56}, {27, 57}, {24,
60}, {66, 102}, {67, 103}, {72, 108}, {73, 109}, {24, 61}, {64, 101}, {65, 100},
{68, 97}, {70, 99}, {25, 63}, {152, 190}, {72, 110}, {73, 111}, {74, 108}, {75,
109}, {25, 62}, {159, 184}, {156, 187}, {155, 188}, {135, 160}, {69, 98}, {71,
96}, {31, 55}, {158, 182}, {157, 181}, {151, 191}, {146, 186}, {145, 185}, {22,
63}, {130, 171}, {28, 53}, {23, 62}, {72, 97}, {73, 96}, {74, 99}, {75, 98},
{30, 52}, {131, 169}, {22, 61}, {150, 189}, {143, 164}, {29, 54}, {23, 60},
{129, 170}, {28, 48}, {143, 163}, {142, 162}, {128, 172}, {31, 50}, {29, 51},
{30, 49}, {148, 187}, {147, 188}, {143, 160}, {142, 161}, {24, 45}, {25, 44},
{16, 38}, {17, 39}, {18, 37}, {25, 46}, {24, 47}, {19, 36}, {139, 179}, {16,
41}, {139, 178}, {19, 42}, {18, 43}, {17, 40}, {74, 112}, {75, 113}, {138, 177},
{138, 180}, {52, 116}, {53, 117}, {42, 107}, {51, 114}, {50, 115}, {46, 111},
{43, 106}, {40, 106}, {55, 117}, {54, 116}, {41, 107}, {45, 110}, {49, 114},
{48, 115}, {44, 100}, {47, 103}, {26, 83}, {27, 82}, {26, 80}, {27, 81}, {45,
102}, {46, 101}, {15, 67}, {37, 105}, {36, 104}, {15, 66}, {58, 119}, {59, 118},
{14, 64}, {39, 105}, {38, 104}, {14, 65}, {56, 119}, {57, 118}, {17, 64}, {21,
68}, {20, 69}, {19, 66}, {16, 67}, {21, 70}, {20, 71}, {18, 65}, {16, 68}, {49,
101}, {43, 127}, {17, 69}, {18, 71}, {149, 192}, {55, 98}, {54, 99}, {53, 96},
{52, 97}, {50, 103}, {40, 125}, {19, 70}, {42, 124}, {48, 102}, {41, 126}, {51,
100}, {20, 76}, {29, 69}, {28, 68}, {20, 77}, {31, 70}, {30, 71}, {23, 78}, {22,
79}, {21, 79}, {23, 77}, {22, 76}, {21, 78}, {14, 82}, {38, 122}, {30, 66}, {28,
64}, {15, 83}, {36, 121}, {44, 113}, {14, 80}, {37, 123}, {31, 65}, {29, 67},
{15, 81}, {39, 120}, {47, 112}, {58, 94}, {60, 88}, {61, 89}, {62, 90}, {63,
91}, {56, 93}, {57, 95}, {59, 92}, {167, 192}, {175, 192}, {10, 122}, {41, 88},
{43, 90}, {11, 121}, {40, 91}, {42, 89}, {13, 120}, {8, 127}, {12, 123}, {9,
126}, {39, 95}, {37, 92}, {6, 124}, {36, 94}, {7, 125}, {38, 93}, {6, 134}, {13,
141}, {12, 140}, {11, 139}, {9, 137}, {10, 139}, {6, 132}, {11, 137}, {7, 133},
{12, 136}, {6, 128}, {12, 138}, {7, 129}, {10, 141}, {13, 138}, {11, 140}, {13,
135}, {8, 131}, {9, 130}, {10, 134}, {8, 133}, {9, 132}, {7, 136}, {8, 135},
{44, 129}, {46, 131}, {45, 130}, {47, 128}, {4, 183}, {3, 182}, {2, 181}, {5,
189}, {2, 187}, {5, 188}, {3, 186}, {4, 190}, {2, 191}, {5, 184}, {4, 185}, {3,
192}, {117, 176}, {99, 171}, {120, 176}, {104, 161}, {96, 170}, {98, 169}, {104,
163}, {105, 162}, {107, 160}, {97, 172}, {105, 164}, {111, 162}, {110, 161},
{101, 180}, {112, 163}, {121, 173}, {122, 174}, {123, 175}, {100, 177}, {102,
179}, {103, 178}, {113, 164}, {114, 167}, {115, 166}, {125, 168}, {115, 165},
{126, 166}, {127, 167}, {116, 173}, {124, 165}, {114, 168}, {116, 174}, {117,
175}, {119, 172}, {118, 170}, {119, 171}, {118, 169}, {124, 156}, {85, 180},
{113, 149}, {126, 154}, {84, 177}, {86, 179}, {87, 178}, {125, 155}, {127, 153},
{112, 152}, {123, 147}, {120, 145}, {90, 176}, {121, 146}, {122, 148}, {108,
156}, {91, 175}, {92, 168}, {106, 158}, {107, 159}, {109, 153}, {88, 173}, {108,
154}, {109, 155}, {89, 174}, {106, 157}, {93, 165}, {94, 166}, {95, 167}, {110,
150}, {111, 151} }>;
(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, 8)(7, 9)(10, 13)(11, 12)(14, 15)(16, 17)(18, 19)(20, 21)(22,
23)(24, 25)(26, 27)(28, 29)(30, 31)(32, 34)(33, 35)(36, 37)(38, 39)(40, 41)(42,
43)(44, 45)(46, 47)(48, 51)(49, 50)(52, 55)(53, 54)(56, 57)(58, 59)(60, 63)(61,
62)(64, 67)(65, 66)(68, 69)(70, 71)(72, 75)(73, 74)(76, 78)(77, 79)(80, 81)(82,
83)(84, 86)(85, 87)(88, 91)(89, 90)(92, 94)(93, 95)(96, 99)(97, 98)(100,
102)(101, 103)(104, 105)(106, 107)(108, 109)(110, 113)(111, 112)(114, 115)(116,
117)(118, 119)(120, 122)(121, 123)(124, 127)(125, 126)(128, 131)(129, 130)(132,
133)(134, 135)(136, 137)(138, 139)(142, 143)(145, 148)(146, 147)(149, 150)(151,
152)(153, 156)(154, 155)(157, 160)(158, 159)(161, 164)(162, 163)(165, 167)(166,
168)(169, 172)(170, 171)(173, 175)(174, 176)(177, 179)(178, 180)(181, 183)(182,
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: (2, 5)(3, 4)(6, 7)(8, 9)(10, 12)(11, 13)(14, 15)(16, 18)(17, 19)(20, 21)(24,
25)(28, 30)(29, 31)(32, 35)(33, 34)(36, 39)(37, 38)(40, 42)(41, 43)(44, 47)(45,
46)(48, 49)(50, 51)(52, 53)(54, 55)(56, 59)(57, 58)(60, 62)(61, 63)(64, 66)(65,
67)(68, 71)(69, 70)(72, 73)(74, 75)(76, 79)(77, 78)(80, 83)(81, 82)(84, 87)(85,
86)(88, 90)(89, 91)(92, 93)(94, 95)(96, 97)(98, 99)(100, 103)(101, 102)(104,
105)(106, 107)(108, 109)(110, 111)(112, 113)(114, 115)(116, 117)(118, 119)(120,
121)(122, 123)(124, 125)(126, 127)(128, 129)(130, 131)(132, 133)(134, 136)(135,
137)(138, 139)(140, 141)(145, 146)(147, 148)(149, 152)(150, 151)(153, 154)(155,
156)(157, 159)(158, 160)(161, 162)(163, 164)(165, 168)(166, 167)(169, 171)(170,
172)(173, 176)(174, 175)(177, 178)(179, 180)(181, 184)(182, 183)(185, 186)(187,
188)(189, 191)(190, 192)
c: (1, 22)(2, 63)(3, 79)(4, 76)(5, 61)(6, 54)(7, 55)(8, 65)(9, 67)(10, 48)(11,
66)(12, 49)(13, 64)(14, 135)(15, 137)(16, 126)(17, 120)(18, 127)(19, 121)(20,
185)(21, 186)(23, 142)(24, 184)(25, 181)(26, 144)(27, 143)(28, 141)(29, 132)(30,
140)(31, 133)(32, 136)(33, 188)(34, 187)(35, 134)(37, 167)(38, 166)(40, 176)(42,
173)(44, 169)(45, 178)(46, 177)(47, 171)(50, 148)(51, 147)(52, 156)(53, 155)(56,
152)(57, 164)(58, 163)(59, 149)(60, 159)(62, 157)(68, 154)(69, 145)(70, 146)(71,
153)(74, 172)(75, 170)(77, 161)(78, 162)(80, 150)(81, 158)(82, 160)(83, 151)(84,
111)(85, 182)(86, 183)(87, 110)(88, 107)(89, 189)(90, 106)(91, 191)(92, 192)(93,
190)(94, 104)(95, 105)(96, 109)(97, 108)(98, 129)(99, 128)(100, 131)(101,
138)(102, 139)(103, 130)(112, 119)(113, 118)(114, 123)(115, 122)(116, 124)(117,
125)(165, 174)(168, 175)
d: (1, 14, 144, 20)(2, 64, 149, 71)(3, 65, 151, 69)(4, 80, 150, 76)(5, 82, 152,
77)(6, 66, 148, 68)(7, 78, 147, 81)(8, 79, 145, 83)(9, 67, 146, 70)(10, 52, 156,
48)(11, 54, 154, 50)(12, 62, 155, 57)(13, 63, 153, 59)(15, 133, 21, 132)(16,
128, 19, 130)(17, 192, 18, 191)(22, 185, 26, 135)(23, 188, 27, 136)(24, 104,
119, 107)(25, 109, 118, 138)(28, 134, 30, 187)(29, 186, 31, 137)(32, 143, 33,
142)(34, 140, 35, 141)(36, 171, 41, 47)(37, 176, 40, 167)(38, 172, 42, 45)(39,
175, 43, 168)(44, 73, 169, 180)(46, 75, 170, 177)(49, 164, 53, 157)(51, 162, 55,
158)(56, 160, 61, 161)(58, 159, 60, 163)(72, 165, 179, 174)(74, 166, 178,
173)(84, 131, 85, 129)(86, 190, 87, 189)(88, 112, 94, 184)(89, 110, 93, 183)(90,
125, 95, 123)(91, 127, 92, 120)(96, 181, 101, 113)(97, 124, 102, 122)(98, 182,
100, 111)(99, 126, 103, 121)(105, 117, 106, 114)(108, 115, 139, 116)
e: (1, 16)(2, 67)(3, 68)(4, 41)(5, 38)(6, 74)(7, 80)(8, 77)(9, 179)(10, 171)(11,
45)(12, 61)(13, 58)(14, 129)(15, 191)(17, 118)(18, 25)(19, 144)(20, 131)(21,
192)(22, 123)(23, 127)(24, 140)(26, 125)(27, 120)(28, 182)(29, 181)(30, 111)(31,
113)(32, 109)(33, 138)(34, 105)(35, 106)(36, 150)(37, 63)(39, 57)(40, 59)(42,
152)(43, 62)(44, 65)(46, 71)(47, 156)(48, 158)(49, 73)(50, 164)(51, 177)(52,
162)(53, 180)(54, 157)(55, 75)(56, 155)(60, 153)(64, 170)(66, 151)(69, 169)(70,
149)(72, 146)(76, 147)(78, 167)(79, 175)(81, 176)(82, 145)(83, 168)(84, 114)(85,
117)(86, 132)(87, 133)(88, 185)(89, 136)(91, 92)(93, 188)(94, 135)(96, 101)(97,
186)(99, 134)(102, 137)(103, 187)(104, 189)(107, 190)(108, 128)(110, 121)(112,
124)(115, 143)(116, 142)(119, 141)(122, 184)(126, 183)(130, 139)(148, 178)(154,
172)(159, 174)(160, 166)(161, 173)(163, 165)
C4[ 192, 193 ]
192
-1 2 3 4 5
-2 187 1 191 181
-3 1 192 182 186
-4 1 190 183 185
-5 1 188 189 184
-6 132 134 124 128
-7 133 125 136 129
-8 133 135 127 131
-9 132 126 137 130
-10 122 134 139 141
-11 121 137 139 140
-12 123 136 138 140
-13 135 138 141 120
-14 80 82 64 65
-15 66 67 81 83
-16 67 68 38 41
-17 69 39 40 64
-18 37 71 43 65
-19 66 36 70 42
-20 77 69 71 76
-21 78 68 79 70
-22 79 61 63 76
-23 77 78 60 62
-24 45 47 60 61
-25 44 46 62 63
-26 56 80 59 83
-27 57 58 81 82
-28 68 48 53 64
-29 67 69 51 54
-30 66 49 71 52
-31 55 70 50 65
-32 55 56 49 60
-33 58 61 51 53
-34 57 50 52 63
-35 48 59 62 54
-36 121 104 94 19
-37 123 92 105 18
-38 122 16 93 104
-39 17 105 95 120
-40 91 125 17 106
-41 88 16 126 107
-42 89 124 19 107
-43 90 127 18 106
-44 100 25 113 129
-45 110 24 102 130
-46 111 101 25 131
-47 24 112 103 128
-48 35 102 115 28
-49 101 114 30 32
-50 34 103 115 31
-51 33 100 114 29
-52 34 116 30 97
-53 33 28 117 96
-54 99 35 116 29
-55 117 31 32 98
-56 26 93 119 32
-57 34 27 95 118
-58 33 27 94 119
-59 35 26 92 118
-60 88 23 24 32
-61 22 33 89 24
-62 23 35 90 25
-63 22 34 25 91
-64 101 14 17 28
-65 100 14 18 31
-66 102 15 19 30
-67 15 103 16 29
-68 16 28 97 21
-69 17 29 20 98
-70 99 19 31 21
-71 18 30 96 20
-72 110 97 108 87
-73 111 84 96 109
-74 99 112 86 108
-75 113 85 98 109
-76 22 93 20 86
-77 23 94 20 87
-78 23 84 95 21
-79 22 92 85 21
-80 89 14 26 87
-81 90 15 27 85
-82 88 14 27 86
-83 91 15 26 84
-84 78 177 83 73
-85 79 81 180 75
-86 179 82 74 76
-87 77 178 80 72
-88 60 82 41 173
-89 80 61 42 174
-90 176 81 62 43
-91 83 40 63 175
-92 79 168 37 59
-93 165 56 38 76
-94 77 166 36 58
-95 78 57 167 39
-96 71 170 73 53
-97 68 72 172 52
-98 55 69 169 75
-99 70 171 74 54
-100 44 177 51 65
-101 46 180 49 64
-102 66 45 179 48
-103 67 178 47 50
-104 36 38 161 163
-105 37 39 162 164
-106 157 158 40 43
-107 159 160 41 42
-108 154 156 72 74
-109 155 73 75 153
-110 45 72 150 161
-111 46 73 151 162
-112 47 74 152 163
-113 44 149 75 164
-114 167 168 49 51
-115 165 166 48 50
-116 52 173 174 54
-117 55 176 53 175
-118 57 59 169 170
-119 56 58 171 172
-120 176 13 145 39
-121 11 36 146 173
-122 38 148 174 10
-123 12 37 147 175
-124 165 156 6 42
-125 155 168 7 40
-126 154 166 41 9
-127 167 8 43 153
-128 47 146 6 172
-129 44 145 170 7
-130 45 148 171 9
-131 46 147 169 8
-132 145 147 6 9
-133 146 148 7 8
-134 157 6 149 10
-135 13 160 150 8
-136 12 159 7 152
-137 11 158 151 9
-138 12 177 13 180
-139 11 178 179 10
-140 11 12 156 153
-141 154 155 13 10
-142 157 159 161 162
-143 158 160 163 164
-144 149 150 151 152
-145 132 129 185 120
-146 121 133 128 186
-147 132 188 123 131
-148 187 122 133 130
-149 144 134 113 192
-150 110 144 189 135
-151 111 144 191 137
-152 144 112 190 136
-153 127 140 185 109
-154 126 108 141 186
-155 188 125 141 109
-156 187 124 140 108
-157 134 181 106 142
-158 143 137 182 106
-159 136 107 184 142
-160 143 135 183 107
-161 110 104 185 142
-162 111 105 142 186
-163 143 188 112 104
-164 143 187 113 105
-165 189 124 93 115
-166 190 115 126 94
-167 114 192 127 95
-168 191 125 92 114
-169 181 118 98 131
-170 182 96 118 129
-171 99 184 119 130
-172 128 183 97 119
-173 88 121 189 116
-174 89 122 190 116
-175 123 91 192 117
-176 90 191 117 120
-177 100 181 138 84
-178 103 139 184 87
-179 102 139 183 86
-180 101 138 182 85
-181 177 2 157 169
-182 3 158 180 170
-183 179 4 160 172
-184 178 5 159 171
-185 145 4 161 153
-186 154 3 146 162
-187 2 156 148 164
-188 155 147 5 163
-189 165 5 150 173
-190 166 4 152 174
-191 176 2 168 151
-192 167 3 149 175
0