[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 189, 9 ] = PS(3,63;17).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {110, 127} under the group generated by the following permutations:

a: (1, 64, 127)(2, 81, 164, 63, 110, 153)(3, 98, 138, 62, 93, 179)(4, 115, 175, 61, 76, 142)(5, 69, 149, 60, 122, 168)(6, 86, 186, 59, 105, 131)(7, 103, 160, 58, 88, 157)(8, 120, 134, 57, 71, 183)(9, 74, 171, 56, 117, 146)(10, 91, 145, 55, 100, 172)(11, 108, 182, 54, 83, 135)(12, 125, 156, 53, 66, 161)(13, 79, 130, 52, 112, 187)(14, 96, 167, 51, 95, 150)(15, 113, 141, 50, 78, 176)(16, 67, 178, 49, 124, 139)(17, 84, 152, 48, 107, 165)(18, 101, 189, 47, 90, 128)(19, 118, 163, 46, 73, 154)(20, 72, 137, 45, 119, 180)(21, 89, 174, 44, 102, 143)(22, 106, 148, 43, 85, 169)(23, 123, 185, 42, 68, 132)(24, 77, 159, 41, 114, 158)(25, 94, 133, 40, 97, 184)(26, 111, 170, 39, 80, 147)(27, 65, 144, 38, 126, 173)(28, 82, 181, 37, 109, 136)(29, 99, 155, 36, 92, 162)(30, 116, 129, 35, 75, 188)(31, 70, 166, 34, 121, 151)(32, 87, 140, 33, 104, 177)
b: (2, 63)(3, 62)(4, 61)(5, 60)(6, 59)(7, 58)(8, 57)(9, 56)(10, 55)(11, 54)(12, 53)(13, 52)(14, 51)(15, 50)(16, 49)(17, 48)(18, 47)(19, 46)(20, 45)(21, 44)(22, 43)(23, 42)(24, 41)(25, 40)(26, 39)(27, 38)(28, 37)(29, 36)(30, 35)(31, 34)(32, 33)(65, 126)(66, 125)(67, 124)(68, 123)(69, 122)(70, 121)(71, 120)(72, 119)(73, 118)(74, 117)(75, 116)(76, 115)(77, 114)(78, 113)(79, 112)(80, 111)(81, 110)(82, 109)(83, 108)(84, 107)(85, 106)(86, 105)(87, 104)(88, 103)(89, 102)(90, 101)(91, 100)(92, 99)(93, 98)(94, 97)(95, 96)(128, 189)(129, 188)(130, 187)(131, 186)(132, 185)(133, 184)(134, 183)(135, 182)(136, 181)(137, 180)(138, 179)(139, 178)(140, 177)(141, 176)(142, 175)(143, 174)(144, 173)(145, 172)(146, 171)(147, 170)(148, 169)(149, 168)(150, 167)(151, 166)(152, 165)(153, 164)(154, 163)(155, 162)(156, 161)(157, 160)(158, 159)
c: (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)

(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
C4[ 189, 9 ]
189
-1 126 65 153 164
-2 66 154 165 64
-3 67 155 166 65
-4 66 68 156 167
-5 67 69 157 168
-6 68 70 158 169
-7 69 71 159 170
-8 70 72 160 171
-9 71 73 161 172
-10 72 74 162 173
-11 73 75 163 174
-12 74 76 164 175
-13 77 165 176 75
-14 78 166 177 76
-15 77 79 167 178
-16 78 80 168 179
-17 79 81 169 180
-18 80 82 170 181
-19 81 83 171 182
-20 82 84 172 183
-21 83 85 173 184
-22 84 86 174 185
-23 85 87 175 186
-24 88 176 187 86
-25 89 177 188 87
-26 88 90 178 189
-27 89 91 179 127
-28 90 92 180 128
-29 91 93 181 129
-30 92 94 182 130
-31 93 95 183 131
-32 132 94 96 184
-33 133 95 97 185
-34 134 96 98 186
-35 99 187 135 97
-36 100 188 136 98
-37 99 101 189 137
-38 100 102 127 138
-39 101 103 128 139
-40 102 104 129 140
-41 103 105 130 141
-42 104 106 131 142
-43 132 143 105 107
-44 133 144 106 108
-45 134 145 107 109
-46 110 135 146 108
-47 111 136 147 109
-48 110 112 137 148
-49 111 113 138 149
-50 112 114 139 150
-51 113 115 140 151
-52 114 116 141 152
-53 115 117 142 153
-54 143 154 116 118
-55 144 155 117 119
-56 145 156 118 120
-57 121 146 157 119
-58 122 147 158 120
-59 121 123 148 159
-60 122 124 149 160
-61 123 125 150 161
-62 124 126 151 162
-63 125 64 152 163
-64 144 2 63 173
-65 1 145 3 174
-66 2 146 4 175
-67 176 3 147 5
-68 177 4 148 6
-69 178 5 149 7
-70 179 6 150 8
-71 180 7 151 9
-72 181 8 152 10
-73 11 182 9 153
-74 154 12 183 10
-75 11 155 13 184
-76 12 156 14 185
-77 13 157 15 186
-78 187 14 158 16
-79 188 15 159 17
-80 189 16 160 18
-81 17 127 161 19
-82 18 128 162 20
-83 19 129 163 21
-84 22 20 130 164
-85 165 23 21 131
-86 22 132 166 24
-87 23 133 167 25
-88 24 134 168 26
-89 25 135 169 27
-90 26 136 170 28
-91 27 137 171 29
-92 28 138 172 30
-93 29 139 173 31
-94 30 140 174 32
-95 33 31 141 175
-96 176 34 32 142
-97 33 143 177 35
-98 34 144 178 36
-99 35 145 179 37
-100 36 146 180 38
-101 37 147 181 39
-102 38 148 182 40
-103 39 149 183 41
-104 40 150 184 42
-105 41 151 185 43
-106 44 42 152 186
-107 187 45 43 153
-108 44 154 188 46
-109 45 155 189 47
-110 46 156 48 127
-111 47 157 49 128
-112 48 158 50 129
-113 49 159 51 130
-114 50 160 52 131
-115 132 51 161 53
-116 133 52 162 54
-117 55 134 53 163
-118 56 135 54 164
-119 55 165 57 136
-120 56 166 58 137
-121 57 167 59 138
-122 58 168 60 139
-123 59 169 61 140
-124 60 170 62 141
-125 61 171 63 142
-126 143 1 62 172
-127 110 81 27 38
-128 111 82 28 39
-129 112 83 29 40
-130 113 84 30 41
-131 114 85 31 42
-132 115 86 32 43
-133 33 44 116 87
-134 88 34 45 117
-135 89 35 46 118
-136 90 36 47 119
-137 91 37 48 120
-138 121 92 38 49
-139 122 93 39 50
-140 123 94 40 51
-141 124 95 41 52
-142 125 96 42 53
-143 126 97 43 54
-144 44 55 64 98
-145 99 45 56 65
-146 66 100 46 57
-147 67 101 47 58
-148 68 102 48 59
-149 69 103 49 60
-150 70 104 50 61
-151 71 105 51 62
-152 72 106 52 63
-153 1 73 107 53
-154 2 74 108 54
-155 55 3 75 109
-156 110 56 4 76
-157 77 111 57 5
-158 78 112 58 6
-159 79 113 59 7
-160 80 114 60 8
-161 81 115 61 9
-162 82 116 62 10
-163 11 83 117 63
-164 1 12 84 118
-165 2 13 85 119
-166 3 14 86 120
-167 121 4 15 87
-168 88 122 5 16
-169 89 123 6 17
-170 90 124 7 18
-171 91 125 8 19
-172 92 126 9 20
-173 93 64 10 21
-174 11 22 94 65
-175 66 12 23 95
-176 67 13 24 96
-177 68 14 25 97
-178 69 15 26 98
-179 99 70 16 27
-180 100 71 17 28
-181 101 72 18 29
-182 102 73 19 30
-183 103 74 20 31
-184 104 75 21 32
-185 22 33 105 76
-186 77 23 34 106
-187 78 24 35 107
-188 79 25 36 108
-189 80 26 37 109
0

**************