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