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On this page are computer-accessible forms for the graph C4[ 171, 4 ] = PS(9,19;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {152, 154} under the group generated by the following permutations:

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

(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.

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

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