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On this page are computer-accessible forms for the graph C4[ 165, 1 ] = C_165(1,34).

(I) Following is a form readable by MAGMA:

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

(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.

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&Graph
C4[ 165, 1 ]
165
-1 132 165 2 35
-2 1 133 3 36
-3 2 134 4 37
-4 3 135 5 38
-5 4 136 6 39
-6 5 137 7 40
-7 6 138 8 41
-8 7 139 9 42
-9 8 140 10 43
-10 11 44 9 141
-11 12 45 10 142
-12 11 143 13 46
-13 12 144 14 47
-14 13 145 15 48
-15 14 146 16 49
-16 15 147 17 50
-17 16 148 18 51
-18 17 149 19 52
-19 18 150 20 53
-20 19 151 21 54
-21 22 55 20 152
-22 23 56 21 153
-23 22 154 24 57
-24 23 155 25 58
-25 24 156 26 59
-26 25 157 27 60
-27 26 158 28 61
-28 27 159 29 62
-29 28 160 30 63
-30 29 161 31 64
-31 30 162 32 65
-32 33 66 31 163
-33 34 67 32 164
-34 33 165 35 68
-35 1 34 36 69
-36 2 35 37 70
-37 3 36 38 71
-38 4 37 39 72
-39 5 38 40 73
-40 6 39 41 74
-41 7 40 42 75
-42 8 41 43 76
-43 44 77 9 42
-44 45 78 10 43
-45 11 44 46 79
-46 12 45 47 80
-47 13 46 48 81
-48 14 47 49 82
-49 15 48 50 83
-50 16 49 51 84
-51 17 50 52 85
-52 18 51 53 86
-53 19 52 54 87
-54 55 88 20 53
-55 56 89 21 54
-56 22 55 57 90
-57 23 56 58 91
-58 24 57 59 92
-59 25 58 60 93
-60 26 59 61 94
-61 27 60 62 95
-62 28 61 63 96
-63 29 62 64 97
-64 30 63 65 98
-65 66 99 31 64
-66 67 100 32 65
-67 33 66 68 101
-68 34 67 69 102
-69 35 68 70 103
-70 36 69 71 104
-71 37 70 72 105
-72 38 71 73 106
-73 39 72 74 107
-74 40 73 75 108
-75 41 74 76 109
-76 77 110 42 75
-77 78 111 43 76
-78 44 77 79 112
-79 45 78 80 113
-80 46 79 81 114
-81 47 80 82 115
-82 48 81 83 116
-83 49 82 84 117
-84 50 83 85 118
-85 51 84 86 119
-86 52 85 87 120
-87 88 121 53 86
-88 89 122 54 87
-89 55 88 90 123
-90 56 89 91 124
-91 57 90 92 125
-92 58 91 93 126
-93 59 92 94 127
-94 60 93 95 128
-95 61 94 96 129
-96 62 95 97 130
-97 63 96 98 131
-98 99 132 64 97
-99 100 133 65 98
-100 66 99 101 134
-101 67 100 102 135
-102 68 101 103 136
-103 69 102 104 137
-104 70 103 105 138
-105 71 104 106 139
-106 72 105 107 140
-107 73 106 108 141
-108 74 107 109 142
-109 110 143 75 108
-110 111 144 76 109
-111 77 110 112 145
-112 78 111 113 146
-113 79 112 114 147
-114 80 113 115 148
-115 81 114 116 149
-116 82 115 117 150
-117 83 116 118 151
-118 84 117 119 152
-119 85 118 120 153
-120 121 154 86 119
-121 122 155 87 120
-122 88 121 123 156
-123 89 122 124 157
-124 90 123 125 158
-125 91 124 126 159
-126 92 125 127 160
-127 93 126 128 161
-128 94 127 129 162
-129 95 128 130 163
-130 96 129 131 164
-131 132 165 97 130
-132 1 133 98 131
-133 99 132 2 134
-134 100 133 3 135
-135 101 134 4 136
-136 102 135 5 137
-137 103 136 6 138
-138 104 137 7 139
-139 105 138 8 140
-140 106 139 9 141
-141 107 140 10 142
-142 11 143 108 141
-143 12 144 109 142
-144 110 143 13 145
-145 111 144 14 146
-146 112 145 15 147
-147 113 146 16 148
-148 114 147 17 149
-149 115 148 18 150
-150 116 149 19 151
-151 117 150 20 152
-152 118 151 21 153
-153 22 154 119 152
-154 23 155 120 153
-155 121 154 24 156
-156 122 155 25 157
-157 123 156 26 158
-158 124 157 27 159
-159 125 158 28 160
-160 126 159 29 161
-161 127 160 30 162
-162 128 161 31 163
-163 129 162 32 164
-164 33 165 130 163
-165 1 34 131 164
0

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