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On this page are computer-accessible forms for the graph C4[ 168, 7 ] = C_168(1,71).

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

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

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