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