[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 155, 2 ] = PS(5,31;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {61, 63} under the group generated by the following permutations:

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

(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.

**************

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

**************