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On this page are computer-accessible forms for the graph C4[ 168, 51 ] = UG(ATD[168,81]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {50, 51} under the group generated by the following permutations:

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

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