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

On this page are computer-accessible forms for the graph C4[ 162, 6 ] = CPM(3,2,9,1).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {18, 19} under the group generated by the following permutations:

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

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