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

On this page are computer-accessible forms for the graph C4[ 144, 31 ] = UG(ATD[144,3]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {82, 83} under the group generated by the following permutations:

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

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

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