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