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On this page are computer-accessible forms for the graph C4[ 171, 5 ] = PS(9,19;4).

(I) Following is a form readable by MAGMA:

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

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

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

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