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On this page are computer-accessible forms for the graph C4[ 189, 6 ] = PS(9,21;4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {84, 85} under the group generated by the following permutations:

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

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

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