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

On this page are computer-accessible forms for the graph C4[ 168, 42 ] = UG(ATD[168,66]).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {20, 23}, {145, 148}, {16, 22}, {105, 110}, {83, 91}, {81, 88}, {147, 152}, {33, 44}, {147, 158}, {103, 106}, {146, 156}, {80, 95}, {14, 30}, {42, 58}, {75, 91}, {76, 93}, {13, 31}, {11, 24}, {33, 50}, {14, 27}, {104, 125}, {32, 54}, {1, 22}, {79, 87}, {104, 114}, {71, 92}, {99, 120}, {39, 59}, {99, 127}, {5, 24}, {65, 92}, {105, 116}, {9, 23}, {32, 62}, {67, 93}, {102, 120}, {103, 121}, {35, 60}, {27, 59}, {128, 160}, {86, 118}, {29, 60}, {83, 113}, {131, 160}, {83, 119}, {133, 161}, {81, 116}, {15, 40}, {17, 57}, {31, 55}, {15, 38}, {136, 161}, {82, 123}, {94, 119}, {1, 43}, {19, 57}, {84, 126}, {3, 47}, {22, 58}, {79, 99}, {91, 119}, {13, 34}, {141, 162}, {89, 118}, {79, 127}, {2, 51}, {31, 46}, {9, 56}, {68, 117}, {144, 162}, {145, 163}, {65, 117}, {70, 115}, {146, 167}, {80, 101}, {3, 53}, {81, 105}, {13, 55}, {73, 115}, {78, 116}, {1, 58}, {2, 62}, {10, 55}, {82, 111}, {6, 56}, {84, 106}, {64, 127}, {1, 64}, {43, 106}, {36, 101}, {52, 118}, {10, 73}, {36, 103}, {34, 97}, {22, 85}, {11, 72}, {16, 85}, {10, 76}, {6, 65}, {53, 114}, {52, 115}, {30, 86}, {8, 66}, {54, 124}, {17, 90}, {25, 82}, {20, 95}, {14, 66}, {54, 122}, {26, 87}, {11, 69}, {18, 92}, {27, 75}, {42, 123}, {12, 95}, {18, 65}, {13, 94}, {25, 77}, {56, 108}, {21, 64}, {26, 79}, {63, 106}, {60, 107}, {28, 68}, {63, 103}, {27, 66}, {61, 100}, {4, 94}, {53, 111}, {32, 122}, {48, 107}, {12, 80}, {38, 122}, {26, 70}, {24, 69}, {36, 121}, {63, 98}, {12, 82}, {50, 108}, {62, 96}, {35, 67}, {45, 77}, {24, 121}, {37, 68}, {28, 125}, {2, 96}, {25, 123}, {12, 111}, {14, 109}, {57, 90}, {33, 69}, {60, 90}, {61, 91}, {8, 96}, {49, 89}, {30, 118}, {7, 110}, {44, 69}, {28, 117}, {62, 87}, {6, 108}, {45, 71}, {21, 127}, {40, 67}, {43, 64}, {3, 111}, {29, 113}, {52, 89}, {18, 98}, {37, 85}, {59, 75}, {4, 119}, {30, 109}, {6, 117}, {44, 88}, {5, 112}, {29, 107}, {61, 75}, {17, 102}, {47, 88}, {32, 87}, {4, 124}, {16, 105}, {51, 74}, {35, 90}, {48, 74}, {5, 121}, {34, 94}, {44, 81}, {52, 73}, {16, 110}, {35, 93}, {19, 109}, {55, 73}, {41, 86}, {43, 84}, {28, 157}, {10, 136}, {42, 168}, {31, 157}, {19, 144}, {26, 159}, {15, 137}, {21, 147}, {17, 151}, {2, 138}, {41, 161}, {23, 159}, {21, 152}, {40, 165}, {46, 160}, {5, 138}, {7, 136}, {23, 134}, {8, 154}, {20, 134}, {48, 164}, {9, 159}, {48, 166}, {15, 153}, {19, 132}, {20, 140}, {3, 153}, {18, 137}, {29, 134}, {4, 152}, {11, 151}, {25, 135}, {9, 150}, {49, 145}, {7, 166}, {54, 149}, {33, 133}, {37, 129}, {34, 135}, {49, 148}, {39, 130}, {7, 161}, {37, 141}, {38, 143}, {45, 132}, {8, 163}, {61, 150}, {41, 133}, {46, 131}, {56, 150}, {58, 148}, {38, 137}, {40, 153}, {41, 155}, {51, 129}, {46, 157}, {47, 156}, {39, 147}, {47, 153}, {50, 133}, {53, 130}, {45, 149}, {39, 158}, {51, 138}, {59, 130}, {36, 158}, {50, 142}, {63, 131}, {49, 140}, {57, 132}, {42, 148}, {78, 143}, {101, 164}, {76, 136}, {88, 156}, {68, 129}, {100, 162}, {76, 139}, {92, 155}, {72, 128}, {110, 166}, {77, 132}, {77, 135}, {74, 129}, {86, 155}, {107, 166}, {102, 168}, {120, 168}, {71, 149}, {83, 128}, {123, 168}, {95, 140}, {115, 167}, {89, 140}, {93, 139}, {112, 167}, {85, 141}, {70, 159}, {126, 165}, {71, 155}, {126, 162}, {72, 151}, {78, 145}, {125, 157}, {66, 163}, {70, 167}, {98, 131}, {108, 142}, {112, 146}, {104, 139}, {124, 152}, {67, 165}, {97, 135}, {125, 154}, {72, 160}, {100, 141}, {124, 149}, {98, 137}, {78, 163}, {99, 142}, {74, 164}, {126, 144}, {114, 130}, {84, 165}, {113, 128}, {102, 151}, {100, 150}, {104, 154}, {97, 146}, {80, 164}, {122, 143}, {120, 142}, {113, 134}, {114, 139}, {96, 154}, {112, 138}, {101, 158}, {116, 143}, {97, 156}, {109, 144} }>;

(II) A more general form is to represent the graph as the orbit of {20, 23} under the group generated by the following permutations:

a: (4, 7)(5, 8)(6, 9)(10, 13)(11, 14)(12, 15)(16, 21)(17, 19)(18, 20)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(43, 58)(44, 59)(45, 60)(46, 52)(47, 53)(48, 54)(49, 63)(50, 61)(51, 62)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168)
b: (1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(22, 94)(23, 95)(24, 96)(25, 100)(26, 101)(27, 102)(28, 88)(29, 89)(30, 90)(31, 105)(32, 103)(33, 104)(34, 85)(35, 86)(36, 87)(37, 97)(38, 98)(39, 99)(40, 92)(41, 93)(42, 91)(43, 124)(44, 125)(45, 126)(46, 116)(47, 117)(48, 115)(49, 113)(50, 114)(51, 112)(52, 107)(53, 108)(54, 106)(55, 110)(56, 111)(57, 109)(58, 119)(59, 120)(60, 118)(61, 123)(62, 121)(63, 122)(64, 152)(65, 153)(66, 151)(67, 155)(68, 156)(69, 154)(70, 164)(71, 165)(72, 163)(73, 166)(74, 167)(75, 168)(76, 161)(77, 162)(78, 160)(79, 158)(80, 159)(81, 157)(82, 150)(83, 148)(84, 149)(127, 147)(128, 145)(129, 146)(130, 142)(131, 143)(132, 144)(133, 139)(134, 140)(135, 141)
c: (2, 3)(4, 131)(5, 130)(6, 132)(7, 89)(8, 88)(9, 90)(10, 73)(11, 75)(12, 74)(13, 31)(14, 33)(15, 32)(16, 148)(17, 150)(18, 149)(19, 108)(20, 107)(21, 106)(22, 58)(23, 60)(24, 59)(25, 68)(26, 67)(27, 69)(28, 135)(29, 134)(30, 133)(34, 157)(35, 159)(36, 158)(37, 123)(38, 122)(39, 121)(40, 87)(41, 86)(42, 85)(43, 64)(44, 66)(45, 65)(46, 94)(47, 96)(48, 95)(49, 110)(50, 109)(51, 111)(52, 136)(53, 138)(54, 137)(56, 57)(61, 151)(62, 153)(63, 152)(70, 93)(71, 92)(72, 91)(76, 115)(77, 117)(78, 116)(79, 165)(80, 164)(81, 163)(82, 129)(83, 128)(84, 127)(97, 125)(98, 124)(99, 126)(100, 102)(103, 147)(104, 146)(105, 145)(112, 114)(118, 161)(119, 160)(120, 162)(139, 167)(140, 166)(141, 168)(142, 144)(154, 156)
d: (1, 2)(4, 149)(5, 148)(6, 150)(7, 107)(8, 106)(9, 108)(10, 90)(11, 89)(12, 88)(13, 132)(14, 131)(15, 130)(16, 74)(17, 73)(18, 75)(19, 31)(20, 33)(21, 32)(22, 51)(23, 50)(24, 49)(25, 97)(26, 99)(27, 98)(28, 162)(29, 161)(30, 160)(34, 77)(35, 76)(36, 78)(38, 39)(40, 114)(41, 113)(42, 112)(43, 96)(44, 95)(45, 94)(46, 109)(47, 111)(48, 110)(52, 151)(53, 153)(54, 152)(55, 57)(58, 138)(59, 137)(60, 136)(61, 65)(62, 64)(63, 66)(67, 139)(68, 141)(69, 140)(70, 120)(71, 119)(72, 118)(80, 81)(82, 156)(83, 155)(84, 154)(85, 129)(86, 128)(87, 127)(91, 92)(100, 117)(101, 116)(102, 115)(103, 163)(104, 165)(105, 164)(121, 145)(122, 147)(123, 146)(125, 126)(133, 134)(142, 159)(143, 158)(144, 157)(167, 168)

(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[ 168, 42 ]
168
-1 22 58 64 43
-2 138 51 62 96
-3 111 47 53 153
-4 124 94 119 152
-5 121 24 112 138
-6 56 117 108 65
-7 110 166 136 161
-8 66 154 96 163
-9 23 56 159 150
-10 55 136 73 76
-11 24 69 72 151
-12 111 80 82 95
-13 55 34 94 31
-14 66 27 30 109
-15 38 137 40 153
-16 22 110 105 85
-17 57 90 102 151
-18 92 137 65 98
-19 132 144 57 109
-20 23 134 95 140
-21 147 127 64 152
-22 1 58 16 85
-23 134 159 9 20
-24 11 121 69 5
-25 77 123 135 82
-26 79 70 159 87
-27 66 14 59 75
-28 68 157 125 117
-29 134 113 60 107
-30 14 118 86 109
-31 55 13 46 157
-32 122 62 54 87
-33 44 133 69 50
-34 13 135 94 97
-35 67 90 60 93
-36 121 101 103 158
-37 68 85 129 141
-38 143 122 15 137
-39 59 147 158 130
-40 165 67 15 153
-41 133 155 161 86
-42 123 58 168 148
-43 1 84 106 64
-44 33 88 69 81
-45 77 132 71 149
-46 157 160 31 131
-47 88 156 3 153
-48 166 74 107 164
-49 89 145 148 140
-50 33 133 108 142
-51 2 138 74 129
-52 89 115 73 118
-53 111 3 114 130
-54 122 124 149 32
-55 13 73 31 10
-56 6 150 9 108
-57 132 90 17 19
-58 22 1 148 42
-59 27 39 75 130
-60 35 90 29 107
-61 100 91 150 75
-62 2 96 32 87
-63 103 106 98 131
-64 1 127 21 43
-65 92 6 18 117
-66 14 27 8 163
-67 165 35 93 40
-68 37 28 117 129
-69 11 33 44 24
-70 167 26 115 159
-71 45 155 92 149
-72 11 160 128 151
-73 55 115 52 10
-74 48 51 129 164
-75 91 59 27 61
-76 136 93 139 10
-77 132 45 25 135
-78 143 145 116 163
-79 99 26 127 87
-80 12 101 95 164
-81 44 88 105 116
-82 12 111 123 25
-83 91 113 128 119
-84 165 126 106 43
-85 22 37 16 141
-86 155 30 41 118
-87 79 26 62 32
-88 44 156 47 81
-89 49 52 118 140
-90 35 57 60 17
-91 61 83 75 119
-92 155 71 18 65
-93 67 35 139 76
-94 34 13 4 119
-95 12 80 140 20
-96 154 2 62 8
-97 34 156 135 146
-98 137 18 63 131
-99 79 127 120 142
-100 61 150 162 141
-101 36 80 158 164
-102 168 17 151 120
-103 121 36 106 63
-104 154 114 125 139
-105 110 81 16 116
-106 103 84 63 43
-107 166 48 60 29
-108 56 6 50 142
-109 144 14 19 30
-110 166 16 105 7
-111 12 3 82 53
-112 167 146 5 138
-113 134 83 29 128
-114 104 139 53 130
-115 167 70 73 52
-116 143 78 81 105
-117 68 6 28 65
-118 89 30 52 86
-119 91 4 83 94
-120 99 102 168 142
-121 24 36 103 5
-122 143 38 32 54
-123 25 168 82 42
-124 4 149 152 54
-125 154 157 104 28
-126 165 144 84 162
-127 99 79 64 21
-128 113 72 83 160
-129 68 37 51 74
-130 59 114 39 53
-131 46 160 63 98
-132 77 45 57 19
-133 33 50 161 41
-134 23 113 29 20
-135 77 34 25 97
-136 7 161 10 76
-137 15 38 18 98
-138 2 112 5 51
-139 114 93 104 76
-140 89 49 95 20
-141 100 37 85 162
-142 99 50 108 120
-143 78 122 38 116
-144 126 19 162 109
-145 78 49 148 163
-146 112 156 167 97
-147 158 39 152 21
-148 145 58 49 42
-149 45 124 71 54
-150 56 100 61 9
-151 11 102 17 72
-152 124 4 147 21
-153 3 47 15 40
-154 125 104 8 96
-155 92 71 41 86
-156 88 47 146 97
-157 46 125 28 31
-158 101 36 147 39
-159 23 26 70 9
-160 46 72 128 131
-161 133 136 7 41
-162 100 144 126 141
-163 66 78 145 8
-164 101 80 48 74
-165 67 126 40 84
-166 110 48 7 107
-167 112 146 70 115
-168 123 102 42 120
0

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