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

On this page are computer-accessible forms for the graph C4[ 168, 40 ] = UG(ATD[168,64]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

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

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