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

On this page are computer-accessible forms for the graph C4[ 168, 4 ] = C_168(1,41).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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