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On this page are computer-accessible forms for the graph C4[ 171, 3 ] = PS(9,19;2).

(I) Following is a form readable by MAGMA:

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

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

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