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