Graph forms
for C4 [ 192, 44 ] =
PL(LoPr_24(3,8,6,8,9),[6^16,8^12])
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On this page are computer-accessible forms for the graph C4[ 192, 44 ] =
PL(LoPr_24(3,8,6,8,9),[6^16,8^12]).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {96, 114}, {96, 120}, {93, 125}, {69, 103}, {65, 98}, {77, 110},
{89, 125}, {70, 99}, {92, 121}, {85, 112}, {71, 98}, {82, 116}, {74, 109}, {95,
120}, {66, 106}, {75, 98}, {73, 99}, {95, 117}, {86, 124}, {84, 120}, {94, 114},
{64, 109}, {67, 109}, {87, 121}, {83, 124}, {90, 117}, {64, 112}, {69, 119},
{66, 113}, {71, 115}, {80, 100}, {70, 115}, {67, 116}, {92, 107}, {89, 110},
{75, 124}, {77, 117}, {91, 98}, {93, 100}, {72, 116}, {87, 107}, {82, 110}, {65,
124}, {94, 99}, {86, 107}, {61, 125}, {39, 102}, {36, 102}, {51, 113}, {46,
106}, {60, 120}, {49, 116}, {63, 121}, {43, 108}, {53, 114}, {44, 100}, {59,
115}, {37, 108}, {46, 103}, {56, 113}, {58, 115}, {52, 126}, {33, 108}, {35,
110}, {57, 119}, {53, 100}, {56, 106}, {37, 112}, {62, 107}, {35, 117}, {33,
121}, {58, 99}, {49, 109}, {39, 122}, {52, 105}, {44, 114}, {57, 103}, {30,
126}, {7, 101}, {31, 125}, {25, 123}, {10, 104}, {4, 97}, {19, 118}, {24, 126},
{6, 97}, {29, 122}, {23, 112}, {6, 111}, {12, 101}, {13, 103}, {16, 122}, {2,
105}, {28, 119}, {14, 101}, {4, 111}, {13, 97}, {2, 111}, {28, 113}, {18, 127},
{1, 111}, {5, 106}, {7, 104}, {22, 102}, {10, 123}, {25, 104}, {5, 118}, {9,
122}, {8, 123}, {11, 127}, {3, 118}, {20, 97}, {1, 119}, {19, 101}, {9, 126},
{30, 105}, {3, 123}, {12, 118}, {23, 108}, {29, 102}, {2, 127}, {21, 104}, {1,
127}, {22, 105}, {20, 148}, {41, 169}, {45, 172}, {57, 184}, {3, 129}, {32,
162}, {27, 153}, {26, 152}, {16, 146}, {18, 150}, {48, 180}, {52, 176}, {56,
188}, {62, 186}, {15, 138}, {42, 175}, {55, 178}, {21, 146}, {32, 167}, {52,
179}, {5, 141}, {42, 162}, {27, 147}, {23, 159}, {20, 156}, {8, 128}, {63, 183},
{8, 129}, {21, 159}, {62, 180}, {22, 157}, {39, 172}, {47, 163}, {1, 140}, {40,
165}, {14, 131}, {59, 182}, {3, 141}, {43, 165}, {38, 168}, {31, 145}, {26,
148}, {24, 150}, {9, 135}, {9, 134}, {46, 161}, {15, 128}, {62, 177}, {63, 176},
{26, 138}, {28, 140}, {57, 169}, {80, 192}, {13, 156}, {41, 184}, {38, 183},
{33, 176}, {49, 160}, {17, 131}, {45, 191}, {43, 185}, {31, 141}, {59, 169},
{13, 158}, {42, 185}, {63, 172}, {26, 142}, {28, 136}, {14, 155}, {43, 190},
{40, 189}, {32, 181}, {16, 134}, {15, 152}, {7, 159}, {39, 191}, {27, 131}, {8,
144}, {59, 163}, {20, 142}, {48, 170}, {24, 130}, {55, 173}, {31, 132}, {7,
155}, {11, 150}, {93, 192}, {14, 147}, {23, 137}, {27, 133}, {56, 166}, {15,
144}, {33, 190}, {24, 135}, {17, 177}, {38, 134}, {34, 130}, {35, 130}, {2,
160}, {4, 166}, {51, 145}, {30, 189}, {50, 145}, {54, 149}, {58, 153}, {5, 161},
{45, 137}, {41, 141}, {18, 182}, {55, 147}, {6, 163}, {48, 149}, {47, 138}, {11,
173}, {34, 133}, {40, 143}, {50, 149}, {60, 155}, {61, 154}, {19, 187}, {12,
167}, {36, 143}, {29, 182}, {60, 151}, {54, 154}, {37, 136}, {53, 152}, {25,
183}, {44, 130}, {17, 190}, {17, 161}, {46, 158}, {44, 156}, {32, 144}, {25,
168}, {48, 129}, {16, 162}, {47, 157}, {45, 159}, {53, 134}, {10, 190}, {34,
150}, {22, 160}, {37, 147}, {29, 171}, {58, 140}, {21, 162}, {60, 139}, {4,
188}, {41, 145}, {51, 139}, {11, 178}, {36, 157}, {18, 171}, {12, 181}, {50,
139}, {54, 143}, {61, 132}, {40, 146}, {42, 144}, {10, 177}, {34, 153}, {30,
165}, {50, 137}, {51, 136}, {19, 174}, {61, 128}, {36, 154}, {38, 152}, {35,
156}, {49, 142}, {54, 137}, {55, 136}, {76, 142}, {67, 128}, {84, 151}, {6,
192}, {81, 151}, {84, 146}, {68, 140}, {92, 148}, {79, 135}, {87, 158}, {75,
129}, {65, 138}, {96, 171}, {78, 133}, {70, 139}, {77, 131}, {88, 151}, {78,
158}, {87, 133}, {81, 132}, {96, 181}, {67, 154}, {79, 148}, {92, 135}, {84,
143}, {65, 157}, {88, 132}, {68, 153}, {70, 155}, {75, 149}, {78, 174}, {79,
175}, {69, 164}, {90, 185}, {91, 191}, {73, 172}, {94, 187}, {89, 188}, {85,
179}, {72, 175}, {81, 182}, {66, 170}, {91, 179}, {76, 164}, {80, 184}, {64,
170}, {95, 181}, {88, 178}, {83, 184}, {74, 166}, {86, 186}, {76, 160}, {77,
161}, {71, 169}, {82, 188}, {47, 192}, {85, 164}, {73, 187}, {95, 173}, {81,
163}, {68, 176}, {78, 187}, {94, 171}, {66, 180}, {76, 186}, {79, 185}, {68,
179}, {90, 173}, {74, 189}, {71, 191}, {74, 178}, {72, 177}, {93, 167}, {83,
168}, {72, 180}, {64, 189}, {82, 175}, {83, 174}, {73, 183}, {89, 167}, {88,
166}, {86, 168}, {80, 174}, {69, 186}, {91, 164}, {90, 165}, {85, 170} }>;
(II) A more general form is to represent the graph as the orbit of {96, 114}
under the group generated by the following permutations:
a: (3, 7)(4, 11)(5, 14)(6, 18)(8, 21)(9, 26)(13, 34)(15, 16)(20, 24)(23, 48)(27,
46)(29, 47)(30, 49)(31, 60)(33, 62)(37, 66)(39, 65)(40, 67)(41, 70)(43, 72)(45,
75)(52, 76)(55, 56)(57, 58)(61, 84)(63, 86)(68, 69)(73, 83)(80, 94)(82, 90)(89,
95)(93, 96)(97, 150)(98, 191)(99, 184)(100, 114)(101, 118)(102, 157)(103,
153)(104, 123)(105, 160)(106, 147)(107, 121)(108, 180)(109, 189)(110, 117)(111,
127)(112, 170)(113, 136)(115, 169)(116, 165)(119, 140)(120, 125)(122, 138)(124,
172)(126, 142)(128, 146)(129, 159)(130, 156)(131, 161)(132, 151)(133, 158)(134,
152)(135, 148)(137, 149)(139, 145)(141, 155)(143, 154)(144, 162)(163, 182)(164,
179)(166, 178)(167, 181)(168, 183)(171, 192)(173, 188)(174, 187)(175, 185)(176,
186)(177, 190) (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, 4)(2, 6)(3, 23)(5, 37)(7, 10)(8, 45)(9, 53)(11, 13)(12, 33)(14, 17)(15,
39)(16, 38)(18, 20)(19, 43)(21, 25)(22, 47)(24, 44)(26, 29)(27, 77)(28, 56)(30,
80)(31, 85)(32, 63)(34, 35)(36, 65)(40, 83)(41, 64)(42, 73)(46, 55)(48, 50)(49,
59)(51, 66)(52, 93)(54, 75)(57, 74)(58, 82)(60, 62)(61, 91)(67, 71)(68, 89)(69,
88)(70, 72)(76, 81)(78, 90)(79, 94)(84, 86)(87, 95)(92, 96)(97, 127)(98,
154)(99, 175)(100, 126)(101, 190)(102, 138)(103, 178)(105, 192)(106, 136)(107,
120)(108, 118)(109, 169)(110, 153)(112, 141)(114, 135)(115, 116)(117, 133)(119,
166)(121, 181)(122, 152)(123, 159)(124, 143)(125, 179)(128, 191)(129, 137)(132,
164)(139, 180)(140, 188)(142, 182)(144, 172)(145, 170)(146, 168)(147, 161)(148,
171)(150, 156)(151, 186)(155, 177)(158, 173)(160, 163)(162, 183)(165, 174)(167,
176)(184, 189)(185, 187)
c: (1, 2)(3, 8)(4, 6)(5, 15)(7, 21)(9, 27)(10, 25)(11, 18)(12, 32)(13, 20)(14,
16)(17, 38)(19, 42)(22, 28)(23, 45)(24, 34)(26, 46)(29, 55)(30, 58)(31, 61)(33,
63)(35, 44)(36, 51)(37, 39)(40, 70)(41, 67)(43, 73)(47, 56)(48, 75)(49, 57)(50,
54)(52, 68)(53, 77)(59, 74)(60, 84)(62, 86)(64, 71)(65, 66)(69, 76)(72, 83)(78,
79)(80, 82)(81, 88)(85, 91)(87, 92)(89, 93)(90, 94)(95, 96)(98, 170)(99,
165)(100, 110)(101, 162)(102, 136)(103, 142)(105, 140)(106, 138)(108, 172)(109,
169)(112, 191)(113, 157)(114, 117)(115, 189)(116, 184)(118, 144)(119, 160)(122,
147)(124, 180)(126, 153)(128, 141)(131, 134)(133, 135)(139, 143)(145, 154)(146,
155)(148, 158)(152, 161)(163, 166)(168, 177)(171, 173)(174, 175)(178, 182)(183,
190)(185, 187)(188, 192)
d: (2, 28)(3, 16)(4, 68)(5, 9)(6, 58)(7, 15)(8, 21)(10, 42)(11, 69)(12, 38)(13,
34)(14, 26)(17, 79)(18, 57)(19, 53)(20, 27)(22, 51)(23, 67)(24, 46)(25, 32)(29,
41)(30, 66)(31, 39)(33, 82)(35, 87)(36, 50)(37, 49)(40, 48)(43, 72)(44, 78)(45,
61)(47, 70)(52, 56)(55, 76)(60, 65)(62, 90)(63, 89)(71, 81)(73, 93)(74, 85)(75,
84)(77, 92)(80, 94)(83, 96)(86, 95)(88, 91)(97, 153)(98, 151)(99, 192)(100,
187)(101, 152)(102, 145)(103, 150)(104, 144)(105, 113)(106, 126)(107, 117)(108,
116)(109, 112)(110, 121)(111, 140)(114, 174)(115, 163)(118, 134)(119, 127)(120,
124)(122, 141)(123, 162)(125, 172)(128, 159)(129, 146)(130, 158)(131, 148)(132,
191)(133, 156)(135, 161)(136, 160)(137, 154)(138, 155)(139, 157)(142, 147)(143,
149)(164, 178)(165, 180)(166, 179)(167, 183)(168, 181)(169, 182)(170, 189)(171,
184)(173, 186)(175, 190)(176, 188)(177, 185)
e: (1, 3, 34, 50, 13, 7)(2, 8, 24, 54, 20, 21)(4, 10, 11, 48, 35, 23)(5, 27, 51,
46, 14, 28)(6, 25, 18, 75, 44, 45)(9, 36, 26, 16, 22, 15)(12, 68, 31, 87, 60,
69)(17, 55, 66, 77, 37, 56)(19, 58, 41, 78, 70, 57)(29, 65, 53, 39, 47, 38)(30,
67, 79, 40, 49, 42)(32, 52, 61, 92, 84, 76)(33, 88, 62, 95, 85, 89)(43, 74, 72,
90, 64, 82)(59, 83, 94, 71, 80, 73)(63, 81, 86, 96, 91, 93)(97, 104, 127, 129,
130, 137)(98, 100, 172, 163, 168, 171)(99, 169, 174)(101, 140, 141, 133, 139,
103)(102, 138, 134)(105, 128, 135, 143, 142, 162)(106, 131, 136)(107, 120, 164,
167, 176, 132)(108, 166, 177, 173, 170, 110)(109, 175, 165)(111, 123, 150, 149,
156, 159)(112, 188, 190, 178, 180, 117)(113, 161, 147)(114, 191, 192, 183, 182,
124)(115, 184, 187)(116, 185, 189)(118, 153, 145, 158, 155, 119)(121, 151, 186,
181, 179, 125)(122, 157, 152)(126, 154, 148, 146, 160, 144)
C4[ 192, 44 ]
192
-1 111 127 140 119
-2 111 105 127 160
-3 123 118 129 141
-4 111 166 188 97
-5 106 161 118 141
-6 111 192 97 163
-7 155 101 104 159
-8 144 123 128 129
-9 122 134 135 126
-10 177 123 190 104
-11 178 127 150 173
-12 101 167 181 118
-13 156 103 158 97
-14 155 101 147 131
-15 144 138 128 152
-16 122 134 146 162
-17 177 190 161 131
-18 127 171 182 150
-19 187 101 118 174
-20 156 148 97 142
-21 146 104 159 162
-22 102 157 105 160
-23 112 137 159 108
-24 135 126 150 130
-25 123 168 104 183
-26 148 138 152 142
-27 133 147 131 153
-28 113 136 140 119
-29 122 102 171 182
-30 165 189 126 105
-31 132 145 125 141
-32 144 167 181 162
-33 121 176 190 108
-34 133 150 130 153
-35 110 156 117 130
-36 143 154 102 157
-37 112 136 147 108
-38 134 168 183 152
-39 122 102 191 172
-40 143 165 189 146
-41 145 169 184 141
-42 144 162 185 175
-43 165 190 108 185
-44 100 156 114 130
-45 191 137 159 172
-46 103 158 106 161
-47 157 192 138 163
-48 180 170 149 129
-49 116 160 109 142
-50 145 137 149 139
-51 145 113 136 139
-52 176 179 126 105
-53 100 134 114 152
-54 143 154 137 149
-55 178 136 147 173
-56 166 188 113 106
-57 103 169 184 119
-58 99 115 140 153
-59 169 115 182 163
-60 155 139 151 120
-61 132 154 125 128
-62 177 180 107 186
-63 121 176 172 183
-64 112 189 170 109
-65 124 157 138 98
-66 113 180 170 106
-67 154 116 128 109
-68 176 179 140 153
-69 103 119 164 186
-70 99 155 115 139
-71 169 191 115 98
-72 177 180 116 175
-73 99 187 172 183
-74 166 178 189 109
-75 124 149 129 98
-76 160 142 164 186
-77 110 117 161 131
-78 187 133 158 174
-79 135 148 185 175
-80 100 192 184 174
-81 132 182 151 163
-82 110 188 116 175
-83 124 168 184 174
-84 143 146 151 120
-85 112 179 170 164
-86 124 168 107 186
-87 121 133 158 107
-88 132 166 178 151
-89 110 188 167 125
-90 165 117 173 185
-91 179 191 98 164
-92 121 135 148 107
-93 100 167 125 192
-94 99 187 114 171
-95 181 117 173 120
-96 114 181 171 120
-97 13 4 6 20
-98 91 71 75 65
-99 58 70 94 73
-100 44 80 93 53
-101 12 14 7 19
-102 22 36 39 29
-103 13 46 57 69
-104 25 7 10 21
-105 22 2 30 52
-106 66 56 46 5
-107 92 62 86 87
-108 33 23 37 43
-109 67 49 74 64
-110 77 89 35 82
-111 1 2 4 6
-112 23 37 85 64
-113 66 56 28 51
-114 44 94 96 53
-115 58 59 70 71
-116 67 49 82 72
-117 77 35 90 95
-118 12 3 5 19
-119 1 57 69 28
-120 60 84 95 96
-121 33 92 63 87
-122 16 39 29 9
-123 3 25 8 10
-124 83 75 86 65
-125 89 93 61 31
-126 24 30 52 9
-127 11 1 2 18
-128 67 15 61 8
-129 3 48 8 75
-130 44 34 24 35
-131 77 14 27 17
-132 88 81 61 31
-133 34 78 27 87
-134 16 38 9 53
-135 24 79 92 9
-136 55 37 28 51
-137 23 45 50 54
-138 47 15 26 65
-139 70 60 50 51
-140 1 68 58 28
-141 3 5 41 31
-142 26 49 20 76
-143 36 40 84 54
-144 15 8 42 32
-145 50 51 41 31
-146 16 40 84 21
-147 55 14 37 27
-148 79 26 92 20
-149 48 50 75 54
-150 11 34 24 18
-151 88 81 60 84
-152 15 26 38 53
-153 34 68 58 27
-154 67 36 61 54
-155 14 70 60 7
-156 44 13 35 20
-157 22 36 47 65
-158 78 13 46 87
-159 23 45 7 21
-160 22 2 49 76
-161 77 46 5 17
-162 16 42 21 32
-163 47 59 81 6
-164 69 91 85 76
-165 90 40 30 43
-166 88 56 4 74
-167 12 89 93 32
-168 25 38 83 86
-169 57 59 71 41
-170 66 48 85 64
-171 94 18 29 96
-172 45 39 73 63
-173 11 55 90 95
-174 78 80 83 19
-175 79 82 72 42
-176 33 68 52 63
-177 17 72 62 10
-178 11 55 88 74
-179 68 91 52 85
-180 66 48 72 62
-181 12 95 96 32
-182 59 81 18 29
-183 25 38 73 63
-184 57 80 83 41
-185 79 90 42 43
-186 69 62 86 76
-187 78 94 73 19
-188 56 89 4 82
-189 40 30 74 64
-190 33 17 10 43
-191 45 91 71 39
-192 47 80 93 6
0