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On this page are computer-accessible forms for the graph C4[ 168, 2 ] = C_168(1,13).

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

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

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