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