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

On this page are computer-accessible forms for the graph C4[ 160, 11 ] = MPS(20,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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