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

On this page are computer-accessible forms for the graph C4[ 168, 16 ] = PS(6,56;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {56, 59} under the group generated by the following permutations:

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

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

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