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On this page are computer-accessible forms for the graph C4[ 160, 15 ] = PS(8,40;9).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 45} under the group generated by the following permutations:

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

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

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