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

On this page are computer-accessible forms for the graph C4[ 144, 30 ] = UG(ATD[144,1]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {76, 79} under the group generated by the following permutations:

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

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

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