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