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